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Geometry Triangle Congruence Day 3 Proving Congruence Name_________________________ Date ______________ Today, we will review how to use a two column proof to prove triangles and parts of triangles are congruent At the end of class, you will be able to complete/fill in proofs using congruence theorems. Proofs proof – A logical argument that shows a ___________________ is ___________. two column proof – has numbered ________________ and corresponding ___________________ that show an argument in a logical order. CPCTC – ________________________ Parts of __________________ Triangles are Congruent. Examples 1. Explain how you can prove that BAD BCD. B A C D N 2. Explain how you can prove that LK PN . M L K P Geometry Proving Congruence in Triangles (continued) Now let’s organize our thoughts into a two column proof! Example 3 Given: X is the midpoint of VY X is the midpoint of WZ Prove: VWX YZX Statements Reasons 1. X is the midpoint of VY 1. 2. X is the midpoint of WZ 2. 3. 3. definition of a midpoint 4. 4. definition of a midpoint 5. VXW YXZ 5. 6. VWX YZX 6. S Example 4 P Given: PR SQ PQ PS Prove: RS RQ Q Statements Reasons 1. PR SQ 1. 2. 3. PR PR R 2. Given 3. 4. 4. 5. 5. E Example 5 Given: Prove: BC EC AB AD DE AD A ABC DEC B C Statements Reasons 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. 7. 7. 8. 8. D