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Objectives: Use triangle congruence to prove corresponding parts are congruent

Section 4-4 Using Congruence Triangle SPI 32C: determine congruence or similarity between triangles SPI 32M: justify triangle congruence given a diagram. Objectives: Use triangle congruence to prove corresponding parts are congruent.

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Objectives: Use triangle congruence to prove corresponding parts are congruent

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  1. Section 4-4 Using Congruence Triangle SPI 32C: determine congruence or similarity between trianglesSPI 32M: justify triangle congruence given a diagram • Objectives: • Use triangle congruence to prove corresponding parts are congruent Corresponding Parts of Congruent Triangles (CPCTC) If you prove triangles congruent (SSS, SAS, AAS, ASA) you can make conclusions about the other parts. By definition corresponding parts of congruent triangles are congruent, abbreviated, CPCTC.

  2. Real-world and CPCTC The giant sinkhole swallowed a house in Winter Park, Florida in 1981 following a drought. The sinkhole formed when the water caverns in the underlying limestone dried up and collapsed. Explain how to use the measurements in the diagram to find the distance across the sinkhole. Since the two triangles are  by SAS, the distance across the sinkhole is 26.5 because CPCTC.

  3. Using CPCTC in a Proof Given: || || Prove: Write a paragraph proof (write proof in complete sentences) Proof: It is given that || || so RPG  PGM and RGP  GPM because alternate interior angles are congruent. Also line PG is congruent to line PG by the reflexive property of congruence. Therefore, by ASA postulate. Since the two triangles are congruent, by CPCTC.

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