College Geometry MTG4212
Fall 2017
Homework 3

Due Friday, October 6, 2017

I. Write proofs of the following exercises on page 16 of the text:  7, 8, 17.  You may use any of the propositions stated or proved in section 1.2.

Hints:

For problem 7:
Let me start by giving the following definition:

Definition: The perpendicular bisector of the straight line AB is the infinite straight line which meets AB at the midpoint of AB, and is perpendicular to AB. Every finite line AB has a perpendicular bisector (this is easy to prove using Propositions 10 and 11 -- you are not required to include a proof of this fact in your HW).

Problem 7 asks you to prove that one set (the locus of all points...) "is" another (the perpendicular bisector of AB).  Proving that two sets are equal generally requires you to write two proofs: prove that each element of the first set is in the second, and that each element of the second is in the first. Applying this principle to the current problem, you should write proofs of the following two statements:
Given a straight line AB:
(i)  For any given point C, prove that if CA = CB, then C is on the perpendicular bisector of AB.
(ii) For any given point C, prove that if C is on the perpendicular bisector of AB, then CA = CB.
Note (i) and (ii) should be two completely separate proofs. Neither should depend in any way on the other.

For problem 8: Use problem 7.

For problem 17: Use the following definition of parallelogram: A parallelogram ABCD is a quadrilateral in which AB is parallel to CD and BC is parallel to AD. (You are not allowed to assume that opposite sides of a parallelogram are equal. If you wish to use this fact, you must first prove it!)

II.  Think about the proofs of 9,10 (do not hand in).

III. Finish reading chapter 1 and start reading 2.1.