Contact Information:My contact information is posted on myweb page.
Office Hours for 2019 - 2020 Fall Semester:8:45am - 9:30am Mon - Fri in Morton 538
Course Description:Intended for Middle Childhood Education majors. Core concepts and principles of Euclidean geometry in two- and three-dimensions. Informal and formal proof. Measurement. Properties and relations of geometric shapes and structures. Symmetry. Transformational geometry. Tessellations. Congruence and similarity. Coordinate geometry. Constructions. Historical development of Euclidean and non-Euclidean geometries including contributions from diverse cultures. Dynamic Geometry Software to build and manipulate representations of two- and three- dimensional objects.
Prerequisites:(MATH 1300 or 1322 or Math placement level 3) and education major
Special Needs:If you have physical, psychiatric, or learning disabilities that require accommodations, please let me know as soon as possible so that your needs may be appropriately met.
Class meetings:Mon, Wed, Fri 9:40am - 10:35am in Morton Hall Room 223
Final Exam Date:Friday, December 13, 2018, 8:00am - 10:00am in Morton 223
Syllabus:For Section 100 (Class Number 7969), taught by Mark Barsamian, this web page replaces the usual paper syllabus. If you need a paper syllabus (now or in the future), unhide the next four portions of hidden content (Textbook, Calendar, Grading, Course Structure) and then print this web page.
Textbook Information:
Textbook Information for 2019 - 2020 Fall Semester MATH 2110
Title:College Geometry, 2ndEdition
Authors:Musser, Trimpe, Maurer
Publisher:Pearson, 2008
ISBN Numbers:
Hardcover ISBN-10:0131879693
Hardcover ISBN-13:978-0131879690
Loose Leaf ISBN-10:0321656776
Loose Leaf ISBN-13:978-0321656773
Calendar:
Calendar for 2019 - 2020 Fall Semester MATH 2110 Section 100 (Class Number 7969), taught by Mark Barsamian
Class Presentations: (Have your presentation written large and clear on paper, ready to project on a document camera.)
Class Presentation: 2.4 # 6 Present a solution to book exercise 2.4 # 6. Figure out which hexominoes can be folded up to form a cube. Present a drawing of all those hexominoes (all on one page). Chose one of those hexominoes and make a big drawing of your that one hexomino, and have it pre-cut and show in class how it can be folded up into a cube.
Class Presentation: Two parts:
Present a solution to book exercise 2.4 # 16abc Which of the drawings in a,b,c is a net for a square pyramid? For the drawings that are, make a big drawing of the net. Have your nets pre-cut and show how they can be folded up into a pyramid.
Draw a net for a square pyramid that isnotone of the drawings in 2.4 # 16abc. Have your net pre-cut and show how it can be folded up into a pyramid.
Class Presentation: 2.4 # 24 Euler Formula for pyramids
Class Presentation: 2.4 # 28 Polyhedron has 10 edges and 6 vertices. How many faces does it have? Sketch a polyhedron that satisfies these conditions and name it.
Take Home Problem:Make a Venn Diagram showing relationship between the following 14 classes of three-dimensional shapes. (These classes are introduced in Section 2.4 of the textbook.) Include one drawing of a sample shape in each region of the diagram.
Polyhedra
Regular Polyhedra
Prisms
Right Prisms
Oblique Prisms
Pyramids
Right Regular Pyramid
Oblique Regular Pyramid
Circular Cylinder
Right Circular Cylinder
Oblique Circular Cylinder
Circular Cone
Right Circular Cone
Oblique Circular Cone.
Week 4: Mon Sep 16 - Fri Sep 20
Day #9:3.1 Perimeter, Circumference, Area of Rectangles & Triangles
Topic:3.1 Perimeter, Circumference, Area of Rectangles & Triangles
Book Section:3.1 Perimeter, Circumference, Area of Rectangles & Triangles
Class Presentations:
Class Presentations:
Class Presentation: (Generalization of 3.1#11 about area, perimeter, circumference, radius of square, circle) (Present your work on the chalkboard.)
First, present an analytical solution, using an unknown areaA.
Then substitute the particular valueA= 25cm2into your general analytical solution to answer the book question.
Class Presentation: (Generalization of 3.1#11 about area, perimeter, circumference, radius of square, circle) (Present your work on the chalkboard.)
First, present an analytical solution, using an unknown areaA.
Then substitute the particular valueA= 18.45cm2into your general analytical solution to answer the book question.
Class Presentation: (Generalization of 3.1#17 about perimeter of rectangle, need to introduce variable) (Present your work on the chalkboard.)
First, present an analytical solution, using an unknown perimeterP
Then substitute the particular valueP= 72cminto your general analytical solution to answer the book question.
Class Presentation: (Generalization of 3.1#18 about area of rectangle, need to introduce variable) (Present your work on the chalkboard.)
First, present an analytical solution, using an unknown areaA
Then substitute the particular valueA= 1440cm2into your general analytical solution to answer the book question.
Class Presentation: (Generalization of 3.1#13b)
Make a large copy of the figure in exercise 3.1#13(b) that you can project using the document camera.
Find the area by using the area of smaller shapes. Explain how you get your answer.
Find the area again, but this time usePick's Theorem(See Exercise 3.1#38). Present your calculation.
Class Presentation about area of region between concentric regular hexagons. Present a solution to a general version of 3.2#14 (on the chalkboard.)
First, present an analytical solution, using an unknown lengthOPand known lengthPQ= 1
Then substitute the particular valueOP= 5.3cminto your general analytical solution to answer the book question.
Class Presentation about area of region created by overlapping circles: Present a solution to a general version of 3.2#16 (on the chalkboard.)
First, present an analytical solution, using an unknown radiusR.
Then substitute the particular valueR= 10.5cminto your general analytical solution to answer the book question.
Class Presentation about area of region created by overlapping circle and square: Present a solution to a general version of 3.2#18a (Present your work on the chalkboard.)
First, present an analytical solution, using an unknown radiusR.
Then substitute the particular valueR= 5cminto your general analytical solution to answer the book question.
Class Presentation about area of region between butting circles: Present a solution to a general version of 3.2#18b (Present your work on the chalkboard.)
First, present an analytical solution, using an unknown radiusR.
Then substitute the particular valueR= 1cminto your general analytical solution to answer the book question.
Class Presentation about area of region created by overlapping circles: Present a solution to a general version of 3.2#19 (Present your work on the chalkboard.)
First, present an analytical solution, using an unknown side lengthx.
Then substitute the particular valuex= 8cminto your general analytical solution to answer the book question.
Day #11:3.3 The Pythagorean Theorem and Right Triangles
Topic:3.3 The Pythagorean Theorem and Right Triangles
Book Section:3.3 The Pythagorean Theorem and Right Triangles
Class Presentations:
Problems about Equilateral Triangles (Present your work on the chalkboard.)
Class Presentation: (Given side length of equilateral triangle, find its area) Present a solution to 3.3#24 (Make a diagram and show the steps clearly.)
Class Presentation: (Given altitude of equilateral triangle, find its area) Present a solution to 3.3#23 (Make a diagram and show the steps clearly.)
Problems about Regular Hexagons (Present your work on the chalkboard.)
Class Presentation: (Given side length for regular hexagon, what is its area?) A regular hexagon has sides of length x. What is the area A of the hexagon? (Make a diagram and show the steps clearly.)
Class Presentation: (Given area for regular hexagon, what is its side length?) A regular hexagon has area A. What is the length x of the sides of the hexagon? (Make a diagram and show the steps clearly.)
Class Presentation: (Given altitude of regular hexagon, find its area) Present a solution to a general version of 3.3#21 (Present your work on the chalkboard.)
First, present an analytical solution, using an unknown distance h. (Make a diagram and show the steps clearly.)
Then substitute particular value \( h = 10\sqrt{3} \) into your general solution to answer book question.
Class Presentation: (Given radius of regular hexagon, find its area) Present a solution to a general version of 3.3#22 (Present your work on the chalkboard.)
First, present an analytical solution, using an unknown radius R (Make a diagram and show the steps clearly.)
Then substitute particular value R=15 into your general solution to answer book question.
A right prism has heighthand has a base that is an equilateral triangle with sides of lengthx. Draw the prism and find its surface area.
Now suppose that the height is 7 and the base has side length 5. Find the surface area.
Ashley Benedict:(Related to 3.4#3a)
A right pyramid has sides with slant heightLand has a base that is an equilateral triangle with sides of lengthx. Draw the pyramid and find its surface area.
Now suppose that the slant height is 7 and the base has side length 5. Find the surface area.
Surface area of right pyramids, one with given slant height and one with given height.
Sam Bernstein:(Similar to 3.4#8a)
A right pyramid has a base that is a square with sides of lengthxand has slant heightL. Draw the pyramid and find its surface area.
Now suppose that the base has side length 5 and the slant height is 7. Find the surface area.
Audrey Brown:(Similar to 3.4#12)
A right pyramid has a base that is a rectangle that has sides of length 2aand 2band has heighth. Draw the pyramid and find its surface area.
Now suppose that the base has sides of length length 10 and 18 and the height is 12. Find the surface area. Give an exact, simplified answer, not a decimal approximation. (Hint: There are some famous triangles involved, whose sides can be determined without a calculator!)
Surface area of right circular cones, one with given slant height and one with given height.
Dominic Buttari:(Similar to 3.4#17a)
A right circular cone has base radius4and has slant heightL. Draw the cone and find its surface area.
Now suppose that the base has radius 5 and the slant height is 13. Find the surface area. Give an exact answer in symbols, and then a decimal approximation.
Kaitlin Cozad:(Similar to 3.4#12)
A right circular cone has base radiusrand has heighth. Draw the cone and find its surface area.
Now suppose that the base has radius 9 and the height is 12. Find the surface area. Give an exact answer in symbols, and then a decimal approximation.
Surface area of sphere
Annie Dill:Present a solution to to 3.4 # 29, but instead of dimensions 1.25 and 1.86 shown in the picture, use numbers 4 and 7. Give an exact answer in symbols. Then give a decimal approximation
Jessie Feilen:(Similar to 3.5#10) A right pyramid has a base that is a regular pentagon that has the following attributes:
The sides of the base have lengthL= 2a
The perpendicular distance from the center of the base to one of its sides isb.
The height ish.
Answer the following questions
Draw the pyramid and find its volume.
Now suppose thata= 5 andb= 18 andh= 12. Find the volume. Give an exact, simplified answer, not a decimal approximation. (Hint: There are some famous triangles involved, whose sides can be determined without a calculator!)
Hanna Gerrard:Present a solution to 3.5 #13 about the volume of right circular cones. For both (a) and (b) of the problem, do the following:
Present an answer in exact, simplified form without using a calculator
Then type your exact answer into a calculator to get a decimal approximation, rounded to two decimal places.
Problems about involving the volume of a hollow shape.
Zack Graham:(based on 3.5 # 41 about volume of rubber in a tennis ball)
Use circumferenceCcm and thicknessTcm.
Use circumferenceC= 22 cm and thicknessT= 0.6 cm. Present the answer as an exact expression that is ready to type into a calculator. (Exact! Not a decimal approximation.) Then type the expression into a calculator to get a decimal approximation rounded to two decimal places.
Katie Henry:Present a solution to 3.5#44 about a steel pipe. Give exact answers in symbols, ready to type into a calculator. Then use a calculator to get decimal approximations rounded to two decimal places
Problems involving Unit Conversions.
Gwen Hoshor:(similar to 3.5#17c) Convert 0.47 ft3to cm3
Present the answer as an exact expression that is ready to type into a calculator. (Exact! Not a decimal approximation.)
Then type the expression into a calculator to get a decimal approximation rounded to two decimal places.
Present the conversion as a single line equation (like we did in class).
You may use the following information: 1 inch = 2.54 centimeters (this is exact).
Amira Hunter:(Related to 3.5#43 about pumping liquid out of a spherical tank)
The book's presentation of the problem says torecall that 1 ft3≈ 7.48 gal. What is the exact conversion? (Show how it is obtained.) (Use the fact that the US gallon is legally defined as 231 cubic inches.)
Present a solution 3.5 # 43 but use diameterDft and liquid volumeGgallons, and use the exact conversion of ft3to gallons that you found in part (a).
Now find the answer whenD= 6 ft liquid volumeG= 200 gallons. Give an exact answer in symbols, ready to type into a calculator. Then use a calculator to get a decimal approximation rounded to two decimal places
Problems involving Scaling.
Matthew McFarland:(similar to 3.5#22) How much do the surface area and volume of a sphere change if its radius is doubled? If its radius is multiplied by some constantk? Explain.
Brianna McFee:(similar to 3.5#23) How do the surface area and volume of a rectangular box change if itslength,width, andheightare all doubled? If they are multiplied by some constantk? Explain.
For Lilly Michigan, Mitchell Myers, Trystan Peyton, Laura Rodgers:Consider the following list of statements that are all namedS:
StatementS: If two angles share a common vertex, then they are adjacent
StatementS: If a polygon is regular, the the polygon has all angles congruent
StatementS: If a polygon has a vertex angle of measure 60, then the polygon is a triangle
StatementS: If a triangle has two angles that are complementary, then the triangle is a right triangle
Answer the following questions
Lilly:Which conditional StatementShas the property thatSis true and the converse ofSis also true? Explain.
Mitchell:Which conditional StatementShas the property thatSis true but the converse ofSis false? Explain.
Trystan:Which conditional StatementShas the property thatSis false but the converse ofSis true? Explain.
Laura:Which conditional StatementShas the property thatSis false and the converse ofSis also false? Explain.
For Conner Singleton, Hannah Six, Lindsay Stanton, Sydney Waugh:Consider the following new list of statements that are also all namedS:
StatementS: If a triangle has reflection symmetry, then the triangle is isosceles
StatementS: Given a triangle with sides of length 2 and 5, If the third side has length 5, then the triangle is isosceles
StatementS: If a triangle has sides 8,13,15, then the triangle is a right triangle
StatementS: If two angles share a common vertex and a common side, then they are adjacent.
Answer the following questions
Conner:Which conditional StatementShas the property thatSis true and the converse ofSis also true? Explain.
Hannah:Which conditional StatementShas the property thatSis true but the converse ofSis false? Explain.
Lindsay:Which conditional StatementShas the property thatSis false but the converse ofSis true? Explain.
Sydney:Which conditional StatementShas the property thatSis false and the converse ofSis also false? Explain.
Tyler Wulf:(The sophisticated problem for today. Sorry.) We have discussed in class the idea the for a conditional statementSof the formIf P then Q, there are three associated conditional statements:
The contrapositive of Sis the statementIf not Q then not P.
The converse of Sis the statementIf Q then P.
The inverse of Sis the statementIf not P then not Q.
We have discussed in class that thecontrapositive of Sis logically equivalent toS. That is, either they are both true, or they are both false.
And we have discussed in class thatconverse of Sis not logically equivalent toS. The truth (or untruth) of one of them tells us nothing about the truth (or untruth) of the other.
But what about theinverse of S? How is the truth ofThe inverse of Srelated to the truth ofSand the truth of thecontrapositive of Sand the truth of theconverse of S? Explain.
Jessie Feilen:Book Problem 4.3#13 is worded as follows:
In triangle \( \Delta ABC \), \( \overline{BD} \) is an altitude of \( \Delta ABC \) and also the bisector of angle \( \angle B \). Prove that \( \overline{BD} \) is the perpendicular bisector of side \( \overline{AC} \).
Here is a more precise wording:
Prove that given any triangle \( \Delta ABC \) with a point \( D \) on side \( \overline{AC} \), if \( \overline{BD} \) bisects angle \( \angle ABC \) and \( \overline{BD} \) is perpendicular to side \( \overline{AC} \), then \( \overline{BD} \) bisects side \( \overline{AC} \).
Do the proof.
Hanna Gerrard:Book Problem 4.3#15 is worded as follows:
Prove that in any isosceles triangle, the median drawn from the vertex angle is the perpendicular bisector of the opposite side.
Here is a more precise wording:
Prove that given any triangle \( \Delta ABC \) with \( \overline{BA} \cong \overline{BC} \) and with a point \( D \) on side \( \overline{AC} \), if \( \overline{BD} \) bisects side \( \overline{AC} \), then \( \overline{BD} \) is perpendicular to side \( \overline{AC} \).
Do the proof.
Zack Graham:Book Problem 4.3#16 is worded as follows:
Prove that in any isosceles triangle, the median drawn from the vertex angle is the bisector of that angle.
Here is a more precise wording:
Prove that given any triangle \( \Delta ABC \) with \( \overline{BA} \cong \overline{BC} \) and with a point \( D \) on side \( \overline{AC} \), if \( \overline{BD} \) bisects side \( \overline{AC} \), then \( \overline{BD} \) bisects angle \( \angle ABC \).
Brianna McFee:(This is book exercise 5.1#33) Prove Corollary 5.2: Given linesLandMcut by a transversalT, ifLandMare both perpendicular toT, then linesLandMare parallel.
Lilly Michigan:(This is book exercise 5.1#34) Prove Corollary 5.3: Given linesLandMcut by a transversalT, if a pair of corresponding angles is congruent, then linesLandMare parallel.
Mitchell Myers:(This is book exercise 5.1#35) Prove Corollary 5.4: Given linesLandMcut by a transversalT, if a pair of interior angles on the same side of the transversal add up to 180, then linesLandMare parallel.
Mark did this one:Prove this statement: Given parallel linesLandM, if a lineTintersects lineL, then lineTalso intersects lineM. (In your proof, you can use any postulate or theorem appearing before Corollary 5.6, which is on page 246.)
Conner Singleton:(This is book exercise 5.1#37) Prove Corollary 5.6: Given lines parallel linesLandM, if a lineTis perpendicular toL, then lineTalso perpendicular to lineM.
Background:Theorems 5.14 through 5.21 in book Section 5.3 are part of (but not all of) the followingMEGA THEOREM. The Six Equivalent Statements Theorem : (Six Equivalent Statements about Convex Quadrilaterals) Given any convex quadrilateral, the following six statements are equivalent (TFAE). That is, they are either all true or all false.
Both pairs of opposite sides are parallel. That is, the quadrilateral is a parallelogram.
Both pairs of opposite sides are congruent.
One pair of opposite sides is both congruent and parallel.
Each pair of opposite angles is congruent.
Either diagonal creates two congruent triangles.
The diagonals bisect each other.
Today we will discuss how to prove such a theorem.
Instructions:
Present on the chalkboard.
The proofs should be very short. But see me for help on Thursday if you are confused.
Remember that in the proof of a theorem or corollary, you are allowed to use any earlier theorem or corollary. For these proofs, you are allowed to use any theorem or corollary numbered up through 5.14. You are not allowed to use Theorems 5.15 through 5.21.)
Laura Rodgers:Your goal is to prove that \( 2 \rightarrow 5 \). Prove the following: Given any convex quadrilateral \( ABCD \), if
\( \overline{AB} \cong \overline{DC} \)
and
\( \overline{AD} \cong \overline{BC} \) then
\( \Delta{ABD} \cong \Delta{CDB} \)
Hannah Six:Your goal is to prove that \( 5 \rightarrow 2 \). Prove the following: Given any convex quadrilateral \( ABCD \), if
\( \Delta{ABD} \cong \Delta{CDB} \) then
\( \overline{AB} \cong \overline{DC} \)
and
\( \overline{AD} \cong \overline{BC} \)
Lindsay Stanton:Your goal is to prove that \( 3 \rightarrow 2 \). Prove the following: Given any convex quadrilateral \( ABCD \), if
\( \overline{AB} \cong \overline{DC} \)
and
\( \overline{AB} \parallel \overline{DC} \) then
\( \overline{AD} \cong \overline{BC} \), Hint: Draw diagonal \( \overline{BD} \). Consider parallel lines \( \overline{AB} \parallel \overline{DC} \) and transversal \( \overline{BD} \). What can you say about some angles based on what you know about those lines? Then somehow show that the two triangles that are created are congruent. Then use that to show that some segments are congruent.
Sydney Waugh:Your goal is to prove that \( 2 \rightarrow 1 \). Prove the following: Given any convex quadrilateral \( ABCD \), if
\( \overline{AB} \cong \overline{DC} \)
and
\( \overline{AD} \cong \overline{BC} \), then quadrilateral \( ABCD \) is aparallelogram. That is,
\( \overline{AB} \parallel \overline{DC} \)
and
\( \overline{AD} \parallel \overline{BC} \) Hint: Draw diagonal \( \overline{BD} \) and then somehow prove that the two triangles that are created are congruent. Then use that to show that some angles are congruent. Then use that to somehow show that some lines are parallel.
Tyler Wulf:Your goal is to prove that \( 1 \rightarrow 5 \). Prove the following: Given any convex quadrilateral \( ABCD \), if quadrilateral \( ABCD \) is aparallelogram, that is, if
\( \overline{AB} \parallel \overline{DC} \)
and
\( \overline{AD} \parallel \overline{BC} \) then
\( \Delta{ABD} \cong \Delta{CDB} \) Hint: Draw diagonal \( \overline{BD} \) Consider parallel lines \( \overline{AB} \parallel \overline{DC} \) and transversal \( \overline{BD} \). What can you say about some angles based on what you know about those lines? Then consider parallel lines \( \overline{AD} \parallel \overline{BC} \) and transversal \( \overline{BD} \). What can you say about some angles based on what you know about those lines? Then prove that the triangles are congruent.
Jenna Baratie:(6.4#34) Triangle \( \Delta ABC \) has right angle at \( \angle C \) and sides \( a,b,c \). Given \( b=8 \) and \( \angle B = 45^{\circ} \), solve for the missing parts. Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.
Ashley Benedict:(6.4#36) Triangle \( \Delta ABC \) has right angle at \( \angle C \) and sides \( a,b,c \). Given \( b=5 \) and \( c=7 \), solve for the missing parts. Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.
Sam Bernstein:(6.4#38) Triangle \( \Delta ABC \) has right angle at \( \angle C \) and sides \( a,b,c \). Given \( a=9 \) and \( \angle B = 41^{\circ} \), solve for the missing parts. Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.
Audrey Brown:(6.4#42) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle A = 22^{\circ} \) and \( b=9.85 \) and \( c=23.6 \), find the area of the triangle. Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.
Dominic Buttari:(6.4#44) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle A \cong \angle B \) and \( \angle C = 48^{\circ} \) and \( c=8 \), find the area of the triangle. Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.
Annie Dill:(6.4#46) Trapezoid \( ABCD \) has \( \overline{AB}=16 \) and \( \overline{CD}=7 \) and \( \overline{DA}=6.4 \) and\( \angle D = 105^{\circ} \) Find the area of the trapezoid. Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.
Jessie Feilen:(6.5#2) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle A = 30^{\circ} \) and \( \angle C = 40^{\circ} \)and \( a=20 \), use theLaw of Sinesto find \( c \). Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.
Hanna Gerrard:(6.5#8) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle B = 75^{\circ} \) and \( b=20 \) and \( c=5 \), use theLaw of Sinesto find \( \angle C \). Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.
Zack Graham:(6.5#12) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle B = 50^{\circ} \) and \( \angle C = 60^{\circ} \)and \( c=10 \), use theLaw of Sinesto find the measures of all remaining parts of \( \Delta ABC \). Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.
Katie Henry:(6.5#18) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle A = 80^{\circ} \) and \( b=9 \) and \( c=10 \), use theLaw of Cosinesto find \( a \). Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.
Gwen Hoshor:(6.5#24) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( a=22 \) and \( b=21 \) and \( c=24 \), use theLaw of Cosinesto find \( \angle A \). Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.
Amira Hunter:(6.5#28) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle B = 80^{\circ} \) and \( a=9 \) and \( c=11 \), use theLaw of Cosinesto find the measures of all remaining parts of \( \Delta ABC \). Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.
Laura Rodgers:Present a solution to problem 7.2#4 on the chalkboard.
Brianna McFee:Present a solution to problem 7.2#12 on the chalkboard. Try to not use Theorem 7.8. Rather, use the general strategy of identifying similar triangles in the figure, and then using the ratios that you get from having similar triangles. That is,
Identify two triangles that you know are similar. Draw them with corrseponding orientation and all known quantities labeled.
Write down the ratios that you get from knowing that the triangles are similar.
Mitchell Myers:Present a solution to problem 7.2#16 on the chalkboard.
Lilly Michigan:Present a solution to problem 7.3#6 on the chalkboard. Give an exact answer first and then a decimal approximation. Try to not use a theorem that tells you about the lengths of the segments. Rather, use the general strategy of identifying similar triangles in the figure, and then using the ratios that you get from having similar triangles. That is,
Identify two triangles that you know are similar. Draw them with corrseponding orientation and all known quantities labeled.
Write down the ratios that you get from knowing that the triangles are similar.
Conner Singleton:Present a solution to problem 7.3#12 on the chalkboard.
Hannah Six:Present a solution to problem 7.3#25 on the chalkboard.
Lindsay Stanton:Problem 7.3#31 Prove Corollary 7.15: If two tangent lines are drawn to a circle from the same point in the exterior of the circle, then the distances from the common point to the points of tangency are equal.
Sydney Waugh:Problem 7.3#32 Prove that if a tangent line and a secant line are parallel, then the arcs that they intercept are congruent.
Tyler Wulf:Prove that if line \( L \) is perpendicular to segment \( \overline{CB} \) at point \( B \), then line \( L \) istangentto the circle that is centered at \( C \) and passes through \( B \). That is, line \( L \) only touches the circle once, at point \( B \).
Day #34:8.1 Coordinates and Distance in the Plane(Quiz 9)
Topic:8.1 Coordinates and Distance in the Plane
Book Section:8.1 Coordinates and Distance in the Plane
Class Presentations: (Class Presentation CP6. I will keep your best 5 of 6 class presentations and drop the lowest one.)
Jenna Baratie:8.1 # 10 about distance formula with variable
Ashley Benedict:8.1 #8 about collinearity test. (Refer to Theorem 8.2) Don�t take time or chalkboard space to show the distance calculations. Just show the results of those calculations and your conclusions.
Sam Bernstein:8.1 # 18 about testing triangles to see if they are right triangles. Your tools should be:
Theorem 4.4 The Converse of the Pythagorean Theorem: If \( a^2 + b^2 = c^2 \), then angle \( \angle C \) is a right angle.
Theorem 3.8 The Pythagorean Theorem (The contrapositive Version)
If \( a^2 + b^2 \neq c^2 \), then angle \( \angle C \)is not a right angle.
Don�t take time or chalkboard space to show the distance calculations. Just show the results of those calculations and your conclusions.
Day #35:8.2 Slope and Starting Section 8.3 Equations of Lines and Circles
Topic:8.2 Slope and Equations of Lines from Section 8.3
Book Section:8.2 Slope and 8.3 Equations of Lines
Class Presentations: (Class Presentation CP6. I will keep your best 5 of 6 class presentations and drop the lowest one.)
Audrey Brown:(Example similar to 8.2 # 27) Find the value of \( a \) so that slope of line segment having endpoints \( (-11,4) \) and \( (a,-3) \) is \( -1/4 \).
Dominic Buttari:(8.2 # 24) Find the slope of a line perpendicular to line \( \overleftrightarrow{AB} \) where
\( A=(0,4) \) and \( B=(-6,-5) \)
\( A=(-1,5) \) and \( B=(-1,3) \)
Annie Dill:(8.2 # 28) Find the value of \( b \) so that the line segment having endpoints \( (5,1) \) and \( (-6,b) \) is perpendicular to the segment having endpoints \( (1,4) \) and \( (-1,0) \).
Jessie Feilen:(8.2 # 29) One diagonal of rhombus \( ABCD \) has vertices \( A=(9,-3) \) and \( C=(6,1) \). Find the slope of the other diagonal.
Hanna Gerrard:(8.3 #24) Find the equations of the perpendicualr bisectors of the sides of the triangle whose vertices are \( (0,0),(4,0),(0,3) \).
Zack Graham:(8.3#26) Find the equation of the altitude line that passes through point \( P \) of triangle \( \Delta PRS \) with vertices \( P=(3,5),R=(-1,1),S=(7,-3) \).
Katie Henry:(8.3 #28c) Use the substitution method to find the simultaneous solution of the system of equations. (Show the steps)
Class Presentations: (Class Presentation CP6. I will keep your best 5 of 6 class presentations and drop the lowest one.)
Lilly Michigan:(8.3#38) Identify the center and radius of each circle whose equation is given.
\( (x-2)^2+(y+5)^2=64 \)
\( (x+3)^2+(y-4)^2=20 \)
Gwen Hoshor:(8.3#40) Write an equation of the circle satisfying each of the following conditions.
Center \( (3,-4) \) and passing through \( (2,-6) \)
Center \( (-2,5) \) and radius \( 7 \)
Endpoints of a diameter at \( (-4,5) \) and \( (12,7) \)
Amira Hunter:(8.3#41) Find the coordinates of thecentroidof the triangle with vertices \( A=(-5,-1), B=(3,3), C=(5,-5)\). (Hint: It is a fact proven in MATH 3110 that in any given triangle, the threemediansof the triangle intersect in a common point. This point is called thecentroid. To find the centroid, one must find the line equations for two of the three median lines, and then use those line equations to determine the point of intersection of those two median lines. The third median line is guaranteed to also pass through this point, so you don't need to find the third median line. See the book page 454, the boxed [Solution of Applied Problem] to see an example of the calculation of the coordinates of the centroid of a triangle.)
Brianna McFee:(8.3#44) Find the coordinates of thecircumscribing circleof the triangle with vertices \( A=(4,5), B=(8,-3), C=(-4,-3)\). (Hint: It is a fact that any threenon-collinearpoints lie on exactly one common circle. That means that given any triangle, there exists exactly one circle that passes through the three vertices of the triangle. One says that this circlecircumscribes the triangle.. Your goal is to find the equation for this circle. The strategy is to
Find the pointPthat is the center of the circle.
Find the radius of the circle
Use the known center and radius to build the equation of the circle.
The key is to notice that pointPwill have the property that \( PA=PB=PC \), because those are the lengths of radial segments. Now consider the equation \( PA=PB \). It tells us that pointPis equidistant from pointsAandB. But then Theorem 4.10, thePerpendicular Bisector Theorem, tells us that pointPmust lie on theperpendicular bisectorof segment \( \overline{AB} \). Similarly, the equation \( PB=PC \) tells us that pointPis equidistant from pointsBandC, and so pointPmustalsolie on theperpendicular bisectorof segment \( \overline{BC} \). So to find the coordinates of pointP, start by finding the line equations for theperpendicular bisectorof segment \( \overline{AB} \) and for theperpendicular bisectorof segment \( \overline{BC} \). Then use those line equations to determine the point of intersection of those two perpendicular bisectors. This point will beP. Once you have pointP, you should be able to compute the circle's radius and build the equation for the circle.)
Week 14: Mon Nov 25 - Fri Nov 29 (Wednesday through Friday is Thanksgiving Break)
Day #37:In-Class Exam 4 Covering Chapters 7 - 8
Wednesday through Friday is Thanksgiving Break: No Class
Week 15: Mon Dec 2 - Fri Dec 6
Day #38:9.1 Isometries and Congruence
Topic:9.1 Isometries and Congruence
Book Section:9.1 Isometries and Congruence
Class Presentations: (Class Presentation CP6. I will keep your best 5 of 6 class presentations and drop the lowest one.)
Mitchell Myers:Present your solutions on graph paper, large and clear, one problem per sheet. If you need graph paper, go to the following link and print some:Graph Paper.
Problem 9.1#6a
Problem 9.1#6b
Problem 9.1#12c
Laura Rodgers:
Part 1: Give the coordinates of the images of the following points under the rotation of \( 90^\circ \) around the origin. (Present your solutions on paper, large and clear, one problem per sheet. If you need graph paper, go to the following link and print some:Graph Paper).
Part 2: We would express the results of the rotation of \( 90^\circ \) around the origin, applied to the point \( (4,2) \), in the following way:
The point \( (4,2) \) rotates \( 90^\circ \) around the origin to the point \( (-2,4) \).
Write sentences that describe the result of the following rotations, and draw a clear picture on blank paper to illustrate each. (One picture per sheet.)
the rotation of \( 180^\circ \) around the origin, applied to the point \( (x,y) \)
the rotation of \( 270^\circ \) around the origin, applied to the point \( (x,y) \)
the rotation of \( 360^\circ \) around the origin, applied to the point \( (x,y) \)
Conner Singleton:(Problem 9.1#36)
Draw \( \Delta ABC \) with \( A=(3,1), B=(4,3), C=(5,-2) \), and draw its image under the reflection with respect to the line \( y=x \) (Illustrate ongraph paper. Be sure to draw the line \( y=x \) and to label all important points with their \( (x,y) \) coordinates.)
If a point \( P=(a,b) \) is reflected across the line \( y=x \), what are the coordinates of the resulting point \( P' \)? (Illustrate on blank paper. Be sure to draw the line \( y=x \) and to label all important points with their \( (x,y) \) coordinates.)
Hannah Six:(9.1#44) Print out the drawing at the following link:9.1#44 Drawing. Use a ruler to draw the reflection line that takes \( \Delta ABC \) to \( \Delta A'B'C' \).
Day #39:9.3 Problem Solving Using Transformations(Quiz 10)
Topic:9.1 Isometries and Congruence
Book Section:9.1 Isometries and Congruence
Class Presentations: (Class Presentation CP6. I will keep your best 5 of 6 class presentations and drop the lowest one.)
Lindsay Stanton:(Present your solution on graph paper, large and clear. If you need graph paper, go to the following link and print some:Graph Paper.) Let triangle \( \Delta ABC \) have vertices \( A=(4,8), B=(7,1), C=(12,3) \) and let triangle \( \Delta DEF \) have vertices \( A=(16,18), B=(19,11), C=(224,13) \). Let \( L \) be the line \( y=10 \) and let \( M \) be the line \( y=20 \). Reflect \( \Delta ABC \) and \( \Delta DEF \) across line \( L \) to get triangles \( \Delta A'B'C' \) and \( \Delta D'E'F' \). Then reflect \( \Delta A'B'C' \) and \( \Delta D'E'F' \) across line \( M \) to get triangles \( \Delta A''B''C'' \) and \( \Delta D''E''F'' \). Draw all six triangles.
Sydney Waugh:(Present your solutions on graph paper, large and clear, one problem per sheet. If you need graph paper, go to the following link and print some:Graph Paper.) Let \( L \) be the line \( y=0 \) and let \( M \) be the line \( y=x \).
Let triangle \( \Delta ABC \) have vertices \( A=(5,-8), B=(10,-8), C=(11,-5) \). Reflect \( \Delta ABC \) across line \( L \) to get triangle \( \Delta A'B'C' \). Then reflect \( \Delta A'B'C' \) across line \( M \) to get triangle \( \Delta A''B''C'' \). Draw all three triangles.
(Start over on a new sheet of graph paper.) Let triangle \( \Delta ABC \) have vertices \( A=(5,2), B=(10,2), C=(11,5) \). Reflect \( \Delta ABC \) across line \( L \) to get triangle \( \Delta A'B'C' \). Then reflect \( \Delta A'B'C' \) across line \( M \) to get triangle \( \Delta A''B''C'' \). Draw all three triangles.
Tyler Wulf:(Present your solution on graph paper, large and clear, one problem per sheet. If you need graph paper, go to the following link and print some:Graph Paper.) Let triangle \( \Delta ABC \) have vertices \( A=(5,2), B=(10,2), C=(11,5) \). Let \( L \) be the line \( y=x \).
Translate \( \Delta ABC \) 10 units to the right to get triangle \( \Delta A'B'C' \) and then reflect triangle \( \Delta A'B'C' \) across line \( L \) to get triangle \( \Delta A''B''C'' \). Draw all three triangles.
(Start over on a new sheet of graph paper.) Reflect triangle \( \Delta ABC \) across line \( L \) to get triangle \( \Delta A'B'C' \) and then translate triangle \( \Delta A'B'C' \) 10 units to the right to get triangle \( \Delta A''B''C'' \). Draw all three triangles.
Exercises:Section 9.3 # 1, 3, 4, 5, 7, 8, 25
Quiz 10
Day #40:Leftovers and Course Review
Topic:Leftovers and Course Review
Book Section:The whole book!
Class Presentations:None!
Exercises:None!
Week 16 (Finals Week): Mon Dec 9 - Fri Dec 13
Day #41: Fri Dec 13
The final Exam is on Friday, December 13, 2019 in Morton 223.
The exam starts after 8:00am, as soon as all your stuff is put away
The exam ends at 10:00am, no exceptions
Bring your Theorem List and your Calculator.
No books, no cell phones.
The Exam is 10 problems
Problem about recognizing a pattern and finding a formula for it
Grading for Section 100 (Class Number 7969), taught by Mark Barsamian
During the semester, you will accumulate aPoints Totalof up to1000 possible points.
Class Presentations:5 presentations @ 20 points each = 100 points possible
Quizzes:Best 8 of 10 quizzes @ 25 points each = 200 points possible
In-Class Exams:Best 3 of 4 exams @ 150 points each = 450 points possible
Final Exam:250 points possible
At the end of the semester, yourPoints Totalwill be converted into yourCourse Letter Grade.
900 - 1000 points = 90% - 100% = A-, A = You mastered all concepts, with no significant gaps.
800 - 899 points = 80% - 89.9% = B-, B, B+ = You mastered all essential concepts and many advanced concepts, but have some significant gaps.
700 - 799 points = 70% - 79.9% = C-, C, C+ = You mastered most essential concepts and some advanced concepts, but have many significant gaps.
600 - 699 points = 60% - 69.9% = D-, D, D+ = You mastered some essential concepts.
0 - 599 points = 0% - 59.9% = F = You did not master essential concepts..
There is no curve.
Throughout the semester, your current scores and current course grade will be available in an online gradebook on the Blackboard system.
Course Structure:
Course Structure for Section 100 (Class Number 7969), taught by Mark Barsamian
One learns math primarily by trying to solve problems. This course is designed to provide structure for you as you learn to solve problems, and to test how well you have learned to solve them. This structure is provided in the following ways.
Exercises:The centerpiece of this course is the list ofExercises, found farther down this web page. The goal of the course is for you to be able to solve the exercises in this table. These exercises are not to be turned in and are not graded, but you should do as many of them as possible and keep your solutions in a notebook for study.The quizzes and exams will be made up of problems similar to suggested exercises.
Reading:To succeed in the course, you will need to read the textbook, study the examples in it. Many of the examples are exactly like exercises on your exercise list. And you will need to read the textbook in order to understand how to do your Presentation Assignments
Office Hours:Come to my office hours for help on your Presentation Assignments and Exercises
Lectures:In lecture, I will sometimes highlight textbook material that is particularly important, sometimes present material in a manner different from the presentation in the book, and sometimes solve sample problems. We have 36 lectures, totaling 1980 minutes. It is not possible to cover the entire content of the course in 1980 minutes, and the lectures are not meant to do that. Lectures are meant to be a supplement to your reading the textbook and solving problems.
Tutoring:Free tutoring is available in the Morton Math Tutoring Lab, in the Math Library, Morton 415a. Make use of it!
Class Presentations:Each of you will be called upon to do fiveClass Presentationsduring the semester. After the first week of class, you will always receive your assignment at least a week before you have to make your presentation. (The Class Presentation Assignments are posted in the Calendar above.) The presentations will involve you presenting a basic example during lecture. The basic examples are always aboutnew material that we will be covering in class that day. To prepare for these Class Presentations, you will need to read the textbook and study its examples. If you are confused about your Class Presentation Assignment, you are welcome to come to my office hours to discuss it. However, before coming to me for help, you need to be sure and read the book and study its examples, and do some work on the assignment. I will not discuss your assignment with you if you have not studied the book.
Quizzes and Exams:The quizzes and exams are based on the list ofExercises, found farther down this web page.
Exercises:
Exercises for Section 100 (Class Number 7969), taught by Mark Barsamian
One learns math primarily by trying to solve problems. The centerpiece of this course is the list of Exercises found in the table below. The goal of the course is for you to be able to solve the exercises in this table. These exercises are not to be turned in and are not graded, but you should do as many of them as possible and keep your solutions in a notebook for study.The quizzes and exams will be made up of problems similar to suggested exercises.
Suggested Exercises for 2019 - 2020 MATH 2110
On all problems: Find an exact answer in symbols first, then find a decimal approximation if one is called for. That is,"EAFTDA".
Section 9.3 Problem Solving Using Transformations # 1, 3, 4, 5, 7, 8, 25
Attendance Policy:
Attendance Policy for Section 100 (Class Number 7969), taught by Mark Barsamian
Attendance is required for all lectures and exams, and will be recorded using sign-in sheets and traditional roll call.
Missing Class:If you miss a class for any reason, it is your responsibility to copy someone's notes or download my notes from the course web page, and study them. I will not use office hours to teach topics discussed in class to students who were absent.
Missing a Quiz or Exam Because of Illness:If you are too sick to take a quiz or exam, then you must
send me an e-mail before the quiz/exam, telling me that you are going to miss it because of illness, then
then go to the Hudson Student Health Center.
Later, you will need to bring me documentation from Hudson showing that you were treated there.
Without those three things, you will not be given a make-up.
Missing Quizzes or Exams Because of University Activity:If you have a University Activity that conflicts with one of our quizzes or exams, you must contact me before the quiz or exam to discuss arrangements for a make-up. I will need to see documentation of your activity. If you miss a quiz or an exam because of a University Activity without notifying me in advance, you will not be given a make-up.
Missing Quizzes or Exams Because of Personal Travel Plans:Many of our quizzes and in-class exams are on Fridays or Mondays. We have an exam on Monday, November 25th. Students often ask me if they can make take a quiz or exam early or late because they have plans to miss a Friday or Monday class in order to lengthen a weekend or a holiday. The answer is always,No you may not take the quiz or exam early or late. You will just have to change your travel plans or forfeit that quiz or exam.
Policy on Cheating:
Policy on Cheating for Section 100 (Class Number 7969), taught by Mark Barsamian
If cheat on a quiz or exam, you will receive a zero on that quiz or exam and I will submit a report to the Office of Community Standards and Student Responsibility (OCSSR).
If you cheat on another quiz or exam, you will receive a grade of F in the course and I will again submit a report to the OCSSR.
Calculators and Free Online Math Resources:
Calculators and Math Websites
Calculators:
Calculators will not be allowed on quizzes or exams.
Websites with Useful Math Resources:
In lectures, I often use a computer for graphing and calculating. The computer tools that I use are free online resources that are easily accessible at the following link.
I use the same online resources in my office, instead of a calculator. You are encouraged to use these same free resources at home, instead of a calculator.
page maintained byMark Barsamian, last updated Dec 6, 2019