1. 2.6 Prove Statements About Segments and Angles

2. Objectives Write proofs involving segment and angle addition
Write proofs involving segment and angle congruence

3. Two-Column Proof Recall what a two-column proof was…
Two-Column Proof – A proof format used in geometry in which an argument is presented with two columns, statements and reasons, to prove conjectures and theorems are true. Also referred to as a formal proof.

4. Two-Column Proof
Statements Reasons
Proof:

5. Example 1: Given: PR = QS Prove the following. Prove: PQ = RS Proof:
Statements Reasons
1. Given
PR = QS 1.
2. Subtraction Property
PR – QR = QS – QR 2.
3. Segment Addition Postulate
PR – QR = PQ; QS – QR = RS 3.
4. Substitution
PQ = RS 4.

6. Your Turn:
Prove the following.
Prove:
Given:

7. Your Turn: Proof: Statements Reasons 1. Given 2. Transitive Property
4. Addition Property
AC = AB, AB = BX
AC = BX
CY = XD
AC + CY = BX + XD
5. Segment Addition Property
AC + CY = AY; BX + XD = BD
AY = BD
6. Substitution 1. 2. 3. 4. 5. 6.

8. Congruence of Segments
Theorem 2.1 (Congruence of Segments)
Congruence of segments is reflexive, symmetric, and transitive.
Reflexive Property: AB  AB
Symmetric Property: If AB  CD, then CD  AB.
Transitive Property: If AB  CD and CD  EF, then AB  EF.

9. Congruence of Angles Theorem 2.2 (Congruence of Angles)
Congruence of angles is reflexive, symmetric, and transitive.
Reflexive Property: A  A
Symmetric Property: If A  B , then B  A
Transitive Property: If A  B and B  C , then A  C .

10. Example 2:
Prove the following.
Prove:
Given:

11. Example 2: Proof: Statements Reasons 1. 1. Given 2.
2. Definition of congruent segments 2.
3. Given 3.
4. Transitive Property 4.
5. Transitive Property 5.

12. Your Turn:
Prove the following.
Prove:
Given:

13. Your Turn: Proof: Statements Reasons 1. Given 2. Transitive Property
5. Symmetric Property 1. 2. 3. 4. 5.

14. Assignment
Geometry: Pg. 116 – 119
#3 – 13, 16, 21, 22