1. GOAL 1 PLANNING A PROOF EXAMPLE 1 4.5 Using Congruent Triangles By definition, we know that corresponding parts of congruent triangles are congruent. So once we have shown that two triangles are congruent by SSS, SAS, ASA, or AAS, we can conclude that all of the remaining pairs of corresponding parts are congruent. We will abbreviate “corresponding parts of congruent triangles are congruent” as CPCTC.

2. by the Alt. Int. Angles Thm. Extra Example 1 H LK J for the same reason. First, show that Then you can use CPCTC to prove that PLAN: PROOF: Reflexive Property we know ASA CPCTC EXAMPLE 2

3. Extra Example 2 MR S A T PLAN: Prove then show that PROOF: StatementsReasons 1. 1. Given 2. 3. 4. 5. 6. Given ASA CPCTC Def. of midpoint EXAMPLE 3

4. Extra Example 3 Q V UTS R PLAN: StatementsReasons 1. 1. Given 2. 3. 4. 5. Reflexive Prop.  Continued on next slide

5. Extra Example 3 (cont.) StatementsReasons 1. 1. Given 2. 3. 4. 5. 6. 7. 8. 9. 10. Reflexive Prop.  Q V U T S R SAS CPCTC Given SAS

6. Checkpoint P N M L Your proof should include the following steps: StatementsReasons 1. 1. Given 2. 3. 4. 5. 6. Reflexive Prop.  Given SAS CPCTC

7. EXAMPLE 4 4.5 Using Congruent Triangles GOAL 2 PROVING CONSTRUCTIONS ARE VALID When proving a construction is valid: You may assume that any two segments constructed using the same compass setting are congruent. You may need to finish drawing a segment which is not part of the actual construction. (See segments BC and EF in Example 4.)

8. Extra Example 4 Write a proof to verify that the construction (copying an angle) is valid. X Y Z M N P StatementsReasons 1. 2. 3. 4. 5. Given SSS CPCTC

9. Checkpoint Prove that the construction of an angle bisector is valid. A D B C StatementsReasons 1. 2. 3. 4. 5. Given Reflexive Prop.  SSS CPCTC