Objective! Use CPCTC to prove parts of triangles are congruent.

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Presentation transcript:

Objective! Use CPCTC to prove parts of triangles are congruent.

CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent.

SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent. Remember!

Example 1: Engineering Application A and B are on the edges of a ravine. What is AB? 1. What do we know? One angle pair is congruent, because they are vertical angles. Two pairs of sides are congruent, because their lengths are equal. 2. How does CPCTC come into play? Therefore the two triangles are congruent by SAS. By CPCTC, the third side pair is congruent, so AB = 18 mi.

Are CPCTC proofs totally different? They are not different AT ALL! There is just one (maybe two) added step(s), which will be your last statement/reason in a two-column proof after you state that the two triangles are congruent.

Z So, we are going to USE: SSS Given: YW bisects XZ, XY  YZ. Example 2: Proving Corresponding Parts Congruent Given: YW bisects XZ, XY  YZ. Prove: XYW  ZYW Z So, we are going to USE: SSS

USE: SSS Z S S S 1. Given 2. Def of segment bisector 3. Given ✔ ✔ ✔ USE: SSS Statements Reasons 1. Given 2. Def of segment bisector S 3. Given S 4. Reflexive S 5. SSS 6. XYW  ZYW 6. CPCTC