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Warm Up Are the following triangles congruent? If so, by which theorem? 1) 2) 3) 4) CPCTC Essential Question: What is CPCTC and how do you use it to prove triangles are congruent? Assessment: Students will demonstrate in writing through two column proofs in their notebooks Key Concept We know that in congruent figures corresponding sides and angles are congruent. This means that once you have shown that two triangles are congruent using SSS, SAS, ASA, AAS, or HL you know that all corresponding sides and all corresponding angles are congruent. – Corresponding Parts of Congruent Triangles are Congruent • Abbreviated CPCTC Essential Question: What is CPCTC and how do you use it to prove triangles are congruent? Assessment: Students will demonstrate in writing through two column proofs in their notebooks Example Tell what theorem shows that the triangles are congruent and list all congruent sides and all congruent angles. Essential Question: What is CPCTC and how do you use it to prove triangles are congruent? Assessment: Students will demonstrate in writing through two column proofs in their notebooks Example Tell what theorem shows that the triangles are congruent and list all congruent sides and all congruent angles. Essential Question: What is CPCTC and how do you use it to prove triangles are congruent? Assessment: Students will demonstrate in writing through two column proofs in their notebooks Key Concept CPCTC is used in proofs after showing that triangles are congruent as a reason for additional sides or angles to be congruent. Essential Question: What is CPCTC and how do you use it to prove triangles are congruent? Assessment: Students will demonstrate in writing through two column proofs in their notebooks Example: Prove the base angles theorem (If two sides of a triangle are congruent then the angles opposite those sides are also congruent.) Given: In ΔABC (AB) ≅(AC) and (BD) is a perpendicular bisector of (BC) Show: ∠B ≅ ∠C Statement Reason 1. AB ≅ AC 1. Given 2. AD ⏊ bisector of BC 2. Given 3. AD ≅ AD 3. Reflexive Property 4. BD ≅ DC 4. Definition of perpendicular bisector 5. ΔABD ≅ ΔACD 5. SSS 6. ∠B ≅ ∠C 6. CPCTC Pierre wishes to prove that ∠R ≅ ∠T in the isosceles triangle shown below. Pierre knows that RS ≅ ST and he drew SU as an angle bisector of ∠RST. Part A: Which triangle congruence postulate would prove that ΔRUS ≅ ΔTUS? Part B: What is the last reason in the proof that proves ∠R ≅ ∠T? Given: ABCD is a parallelogram Prove: (AB) ≅(CD) and (BC) ≅(AD) STATEMENTS REASONS 1 ABCD is a parallelogram 1 Given 2 Draw segment from A to C 2 Two points determine one line 3 𝐴𝐵 ∥ 𝐶𝐷 and 𝐵𝐶 ∥ 𝐴𝐷 3 Definition of Parallelogram 4 ∠1 ≅ ∠2 ∠3 ≅ ∠4 4 Alternate Interior Angles 5 𝐴𝐶 ≅ 𝐴𝐶 5 Reflexive Property 6 ΔABC ≅ ΔCDA 6 7 𝐴𝐵 ≅ 𝐶𝐷, 𝐵𝐶 ≅ 𝐴𝐷 7 ASA CPCTC Essential Question: What is CPCTC and how do you use it to prove triangles are congruent?