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Using Congruent Triangles: CPCTC At the end of this lesson, you should be able to use CPCTC to show that if two triangles are congruent, then all their corresponding sides and angles are congruent. Proving Congruent Triangles: Recall, to prove triangles congruent, we used the following postulates: SSS __________ SAS __________ ASA __________ AAS (SAA) __________ AAA ASS/SSA CPCTC CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. What does CPCTC Mean? It means that once we know that two triangles are congruent, we know that all corresponding (matching) sides and angles are congruent! Use backwards planning here! Example Think: If I can show that ∆ RAD ≡ ∆ AID, then I can show any corresponding part (side or angle) is congruent. A Statement Reason 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. R 1 2 D Given: RA ≡ AI; D is the midpoint of RI; ∠1 ≡ ∠2 Prove: ∠R ≡ ∠I I Use backwards planning here! Think: If I can show that ∆ KON ≡ ∆ RON, then I can show any corresponding part (side or angle) is congruent. Statement Reason K O 1 R 2 1. 1. 2. 2. 3. 3. 4. 4. Given: ∠1 ≡ ∠2; ON bisects ∠ KNR 5. 5. Prove: ∠K ≡ ∠R 6. 6. N Checks for Understanding 1. What four ways do we have two show that two triangles are congruent? 2. For what does CPCTC stand? 3. In your own words, what does CPCTC mean? 4. Before using CPCTC, you must always prove what first? Using CPCTC in Overlapping Figures Recall, a common 2-step method for showing two segments or angles are congruent is to: Show ∆s congruent (SSS, SAS, ASA, AAS) Use CPCTC to show that the corresponding parts (segments or angles are congruent) Is ∠ E ≡ ∠ R? MN ≡ MA; ME ≡ MR E N M E Y A 1. Label. 2. Color. 3. Redraw. R M A Showing Parts Congruent ∆ _____ ≡ ∆ ______ Reason: _______ (SSS, SAS, ASA, AAS) All Corresponding Angles Congruent All Corresponding Sides Congruent ∠ _____ ≡ ∠ _____ ∠ _____ ≡ ∠ _____ ∠ _____ ≡ ∠ _____ _____ ≡ _____ _____ ≡ _____ _____ ≡ _____ Reason: _______ Checks for Understanding In your own words, describe the procedure for showing segments or angles in overlapping figures are congruent. Homework: CPCTC WS, plus text page 205: 7-14 all. Weekly Quiz on Friday, January 11, 2008 4.1- 4.4