### MATH325: Test 1

**Name:**

You may use pencil, pens, ruler, compass and scissors on this test.
You may not use a calculator, book or notes. Please take your time on
each problem and show your work in the space provided. If you get
stuck on a problem, move on to the next and return when you have time.

- (15 points) State the fifth axiom or postulate.

**Name:**

- (25 points) Shown below is a
triangle ABC and a point P. Sketch the result of rotating ABC 90°
clockwise about point P.

**Name:**

- (30 points) Prove that if chord AB is not a diameter of a circle
and if chord CD is the perpendicular bisector of AB, then CD is a
diameter of the circle. (You may assume that if a diameter bisects a
chord which is not a diameter, then the diameter is perpendicular to
the chord.)

**Name:**

- (30 points) Without using the Star Trek Lemma, show that if O is the center of the circle shown below,
the measure of angle BOD is twice the measure of angle BAD.

**Name:**

**Bonus:** (5 points) Prove that the sum of the angle measures of a
triangle is 180°.