D-7 Triangle proofs with CPCTC
Opening question: Look at the triangle proof below. With what is written in the proof, would you be able to
conclude that ∠𝑺 ≅ ∠𝑷? Why or why not?
→Triangle proofs won’t always end with __ __. There are two other ways they could end.
Given: ACB is an isosceles with vertex ∠𝐶 1 2
D is the midpoint of 𝐴𝐵̅̅ ̅̅
Prove: (i) ACD BCD
(ii) 1 2
(iii) 𝐶𝐷̅̅ ̅̅ bisects ACB
Example 1: Write a two-column proof. Do not mark prove statement on picture!
Example 2: Given: CN bisects ∠𝐴𝐶𝐵,
ACB is an isosceles with vertex ∠𝐶
Prove: N is midpoint of AB
Example 3: For the follwowing proof, the statements are out of order. Reorder the statements and provide reasons
for each statement.
Given: Prove: 𝐴𝐷 ≅ 𝐵𝐶
AB || DC
𝐴𝐷 ≅ 𝐵𝐶
∠ABD ≅ ∠CDB
BD ≅ BD
∠A ≅ ∠C
∆ 𝐴𝐵𝐷 ≅ ∆𝐶𝐷𝐵