MATH325: Test 1

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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.

  1. (15 points) State the fifth axiom or postulate.
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  2. (25 points) Shown below is a triangle ABC and a point P. Sketch the result of rotating ABC 90° clockwise about point P.


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  3. (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.)
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  4. (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.

Inscribed and central angles spanning the same arc.
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Bonus: (5 points) Prove that the sum of the angle measures of a triangle is 180°.