1. Chapter 2.6 (Part 1): Prove Statements about Segments and Angles
Goal: You will write proofs using geometric theorems.

2. Example 2. AC = AB + BC 3. AC = AB + AB
Three steps of a proof are shown. Give the reasons for the last two steps.
2. AC = AB + BC
3. AC = AB + AB

3. Example 2. 2. Definition of Angle Bisector 3.
3. Definition of congruent angles
4. m<1 + m<2 = m<ABC 4.

4. Example (cont) 5. 5. Substitution Property of Equality 6. 6. Simplify

5. Example 2. Angle Addition Postulate 3. Angle Addition Postulate 2. 3.
4. m<1 + m<2 = m<3 + m<4 4.

6. Example 6.
6. Substitution Property of Equality
7. m<1 = m<4 7.

7. Example Given: <1 and <2 are a linear pair
Prove: m<2 = 180° - m<1
Statement Reason
1. <1 and <2 are a linear pair
2. <1 and <2 are supplementary
3. m<1 + m<2 = 180°
4. m<1 = 180° - m<2
1. Given
2. The angles in a linear pair are supplementary
3. Def of Supplementary Angles
4.Subtraction Prop of Equality

8. Theorem 2.1:Congruence of Segments
Segment congruence is reflexive, symmetric, and transitive.

9. Theorem 2.2:Congruence of Angles
Angle congruence is reflexive, symmetric, and transitive.

10. Example 1. Given 1. AB = 5 2. Given 2. BC = 5 3. Substitution
Given: AB = 5, BC = 5, BC CA
Prove: AB DE
Statement Reason C B
1. Given
2. Given
3. Substitution
4. Definition of Congruent Segments
5. Given
6. Substitution ( or Transitive)
1. AB = 5
2. BC = 5
3. AB = BC
4. AB BC
5. BC CA
6. AB CA

11. Example 1. <3 and <2 are supplementary. 1. Given
Given: <3 and <2 are supplementary. m <1 + m <2 = 180°
Prove: <1 <3
Statement Reason 1 2 3
1. <3 and <2 are supplementary.
2. m <1 + m <2 = 180°
3. m <3 + m <2 = 180°
4. m <1 + m <2 = m <3 + m <2
5. m <1 = m <3
6. <1 <3
1. Given
2. Given
3. Def. of Supplementary Angles
4. Substitution
5. Subtraction Property
6. Def. of Congruent Angles