Unit 3 Prove Statements about Segments and Angles

1. Unit 3 Prove Statements about Segments and Angles

2. Any geometric object is congruent to itself. AB AB If object a b, then object ba If object ab and object bc, then object ac

3. 1. Write the reason for each statement Reflexive Prop Transitive Prop Symmetric Prop

4. 2. Complete the proof by writing a reason for each step. GIVEN: AL = SK PROVE: AS = LK C. given E. Reflexive Prop F. Addition Prop A. Segment Addition Post. D. Segment Addition Post. B. Substitution Prop

5. 3. Complete the proof. GIVEN: M is the midpoint of , AM = 6in PROVE: AB = 12in given Def. of midpt given Segment Add. Post. Substitution Substitution Combine Like Terms

6. 4. Complete the proof. GIVEN: bisects at O, CO = 9cm PROVE: CD = 18in given Def. of segment bisector given Segment Add. Post. Substitution Substitution Combine Like Terms

7. 5. Complete the proof. GIVEN: bisects ABC, mABD = 20° PROVE: mABC = 40° 1. 1. Given bisects ABC mABD = mDBC 2. 2. Def. of angle bisector mABD = 20° 3. 3. given 4. Angle Addition Prop. 4. mABD + mDBC = mABC 5. Substitution 5. mABD + mABD = mABC 6. Substitution 20° + 20° = mABC 6. 7. Combine Like Terms mABC = 40° 7.

8. HW Problem # 18 D

9. D 1. Given 2. Angle Addition Postulate 3. Substitution 4. Combine Like Terms 5. Addition 6. Division • 1. mABC = 90° • 2. mABD + mDBC = 90° • 6x + 3x – 9 = 90 • 9x – 9 = 90 • 9x = 99 • x = 11