1. Given: Prove: x = 10 1. __________ 1. ___________ 2. __________ 2. ___________ 3. __________ 3. ___________ 4. __________ 4. ___________ StatementsReasons x = 10 Given Substitution Subtraction Multiplication

2. Given: m  4 + m  6 = 180 Prove: m  5 = m  6 1. __________ 1. ___________ 2. __________ 2. ___________ 3. __________ 3. ___________ 4. __________ 4. ___________ 5. __________ 5. ___________ StatementsReasons Given Angle Add. Post. Substitution Reflexive m  4 = m  4 m  4 + m  5 = m  4 + m  6 m  4 + m  5 = 180 m  4 + m  6 = 180 m  5 = m  6 Subtraction

3. Segment Addition Postulate Angle Addition Postulate Definition of a Midpoint Definition of an Angle Bisector Midpoint Theorem Angle Bisector Theorem Definition of Complementary Angles Definition of Supplementary Angles

4. Pieces of a segment add up to the whole segment. Angle Addition Postulate Definition of a Midpoint Definition of an Angle Bisector Midpoint Theorem Angle Bisector Theorem Definition of Complementary Angles Definition of Supplementary Angles

5. Segment Addition Postulate Measure of an  is the sum of the measures of the smaller  s  that make it up Definition of a Midpoint Definition of an Angle Bisector Midpoint Theorem Angle Bisector Theorem Definition of Complementary Angles Definition of Supplementary Angles

6. Segment Addition Postulate Angle Addition Postulate If given a midpoint, it divides a segment into two  segments Definition of an Angle Bisector Midpoint TheoremAngle Bisector Theorem Definition of Complementary Angles Definition of Supplementary Angles

7. Segment Addition Postulate Angle Addition Postulate Definition of a Midpoint If given an  bisector, then it divides the  into 2   s Midpoint TheoremAngle Bisector Theorem Definition of Complementary Angles Definition of Supplementary Angles

8. Segment Addition Postulate Angle Addition Postulate Definition of a Midpoint Definition of an Angle Bisector If you have a midpoint, then each piece is HALF the whole segment Angle Bisector Theorem Definition of Complementary Angles Definition of Supplementary Angles

9. Segment Addition Postulate Angle Addition Postulate Midpoint Theorem Angle Bisector Theorem Midpoint Theorem If you have an  bisector, then the measure of each  is half the whole  Definition of Complementary Angles Definition of Supplementary Angles

10. Segment Addition Postulate Angle Addition Postulate Midpoint Theorem Angle Bisector Theorem Midpoint Theorem Angle Bisector Theorem If given complementary angles, then they sum to 90 ° Definition of Supplementary Angles

11. Segment Addition Postulate Angle Addition Postulate Definition of a Midpoint Definition of an Angle Bisector Midpoint Theorem Angle Bisector Theorem Definition of Complementary Angles If given supplementary  s, then the  sum to 180 °

12. Given: WX=YZ; Y is the midpoint of XZ Prove: WX=XY WY Z X 1.) WX=YZ Y is the midpoint of XZ 2.) XY=YZ 3.) WX=XY 1.) Given 2.) Definition of a midpoint 3.) Substitution

13. Proof of the Midpoint Theorem Given: M is the midpoint of ABProve: AM = ½AB; MB = ½AB 1.2.3.4.5.6. M is the midpoint of AB MB = ½AB AM = MB AM + MB = AB AM + AM = AB 2AM = AB AM = ½AB Given Def. of a Midpoint Segment Add. Post. Substitution Division Property Substitution AMB

14. Given: m<1=m<2 AD bisects <CAB; BD bisects <CBA Prove: m<3=m<4 C B A 1 3 2 4 D 1.) m<1=m<2 AD bisects <CAB; BD bisects <CBA 2.) 3.) 1.) Given 2.) Definition of an Angle Bisector 3.) Substitution

15. Proof of the  Bisector ThmProve: m  ABX = ½m  ABC and m  XBC = ½m  ABC. Given: BX is the bisector of  ABC. B C X A 1. BX is the bisector of  ABC. 1. Given 2. m  ABX = m  XBC2. Def. of an angle bisector 3. m  ABX + m  XBC = m  ABC3. Angle Add. Post. 4. m  ABX + m  ABX = m  ABC 2m  ABX = m  ABC 4. Substitution 5. m  ABX = ½m  ABC5. Division Property 6. m  XBC = ½m  ABC6. Substitution