Math 444 Quiz 1

Do Problem 1 and Problem 2 (a construction problem on the back).

Problem 1

Prove ONE of the following.  Do not do both.  If you work on both, cross out the one you do not want graded.

• Prove that a point C is on the perpendicular bisector of segment AB if and only if AC = BC.  [For the proof you may assume the basic axioms plus the 3 congruence criteria SAS, ASA, SSS.]
• Prove that ABCD is a parallelogram if and only if the diagonals bisect each other. [For the proof, you may assume the basic axioms plus the 3 congruence criteria SAS, ASA, SSS and the fundamental theorem about angles formed by 2 parallels and a transversal.]
  

Problem 2

The following is a compass and straightedge construction.  Use a compass and straightedge (without using the marks on your ruler).  Write succinctly the important steps of your construction.  Use labels on important points, circles and lines to make the explanation clearer.  You do NOT have to justify your methods.  Just make it clear what you did.

• Given a line AB and a point C, construct a point D so that line CD is parallel to AB.