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.

Sample Proof:

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

Statements Reasons

AB || DC

𝐴𝐷 ≅ 𝐵𝐶

∠ABD ≅ ∠CDB

BD ≅ BD

∠A ≅ ∠C

∆ 𝐴𝐵𝐷 ≅ ∆𝐶𝐷𝐵