Download Instructor: Dr. Alexandra Shlapentokh

Assignments for Mathematics 3233-001
College Geometry
Fall 2007
T, Th 11:00 AM - 12:15 PM, Austin 204
Instructor: Dr. Alexandra Shlapentokh
Class 1, 8/23/07.
Homework # 1: 1–5, page 17.
Class 2, 8/28/07.
No new homework
Class 3, 8/30/07.
Homework # 2: 10, 11, page 17.
Class 4, 9/04/07.
Homework # 3: 2, 5, page 25. The definition of a concrete model is on page 15.
Class 5, 9/06/07.
Homework # 4: 5, page 31. Hints: (i) Can you construct a model for this geometry? (ii) Can you have
a “similar” geometry with 4 points? (iii) Can you have a model without parallel lines? with parallel lines?
Does a line have to pass through at least one point? (iv) Do all lines have to be “straight”? All points can
be collinear.
Class 6, 9/11/07.
Study Guide #1.
Class 7, 9/13/07.
Test #1.
Class 8, 9/18/07.
Homework # 5: 3, p.64.
Class 9, 9/20/07.
Homework # 6: Let A, B be two distinct points. Show that we can use the SMSG Postulates 3 and 4 so
that A is assigned a positive number and B is assigned a negative number.
Class 10, 9/25/07.
Homework # 7: Prove the following proposition: Let A, B, C be three distinct collinear points with A−B−C.
Let yA , yB , yC be the numbers assigned to A, B, C respectively under the Ruler Postulate (Postulate #3).
Prove yA < yB < yC or yC < yB < yA .
Class 11, 9/27/07.
Homework # 8: Prove the following proposition: Let A, B be distinct points. Let O ∈ AB. Let ` be any
line passing through O. Show that A and B will belong to two different half-planes fromed by `.
Class 12, 10/2/07.
Homework # 9: Write down details of the proof of existence and uniqueness of the mid-point of a segment.
1
Class 13, 10/4/07.
Study Guide #2.
Class 14, 10/9/07.
Test #2.
Class 15, 10/11/07.
Homework # 10: 8, page 89.
Class 16, 10/18/07.
Homework # 11: 1, page 94.
Class 17, 10/23/07.
Homework # 12: 10, page 94.
Class 18, 10/25/07.
Homework # 13: Rewrite the class proof of Theorem 3.2.9 for another angle. Use the same notation and
picture as in class.
Class 19, 10/30/07.
Homework # 14: Prove the following assertions:
(1) Let AB and CD be two segments such that the distance from A to B is greater than the distance
from C to D. Show that there exists B 0 ∈ AB such that m(AB 0 ) = m(CD).
(2) Let AB and CD be two segments such that the distance from A to B is greater than the distance
~ such that m(AB) = m(CD0 ).
from C to D. Show that there exists D0 ∈ CD
(3) Let A, B, C be three non-collinear points. Let D ∈ AC. Show that D is in the interior of ∠ABC.
Homework # 15: Prove the following propositions:
(1) Let A, B, C, D be points such that no three are collinear and such that C and D are in the same
←→
half-plane with respect to AB. Then either C is in the interior of ∠BAD or D is in the interior of
∠BAC.
D
·
C
·
·
B
A
←→
Hint: Suppose D is not in the interior of ∠BAC. Then B and D are on different sides of AC (explain
←→
why). So BD intersects AC (why?). By the HW #14, Problem #3, this intersection is a point in the
~ contains a point in the interior of ∠BAD and the whole ray AC
~ \ {A}
interior of ∠BAD. Thus AC
is in the interior of ∠BAD (why?).
(2) Let A, B, C, D be as above and assume that m(∠BAD) > m(∠BAC). Then C is in the interior of
∠BAD by angle addition postulate (why?).
2
Class 20, 11/6/07.
Study Guide #3.
Class 21, 11/8/07.
Test #3.
Class 22, 11/13/07.
Homework # 16: 1, page 101.
Class 23, 11/15/07.
Homework # 17: 6, page 102.
Class 24, 11/20/07.
Homework # 18: 3, page 135.
Class 25, 11/27/07.
Homework # 19: 6, page 135.
Class 26, 11/29/07.
No new homework
Class 27, 12/4/07.
Final Study Guide.
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