Question

Attachment.

Answer 1

Draw in the line segments to create triangle
BPC

and triangle AQC

Answer 2

I know it has to do with the isosceles triangle theorem, but I'm not sure how to write a proof about it.

Answer 3

and label the angles and sides that are congruent

Answer 4

I make it 2 diagrams, otherwise it is hard to visualize

Answer 5

Oh.....I get it. You have to prove it by SAS postulate kind of.

Answer 6

You don't mean SAS , do you?

I marked what we know....

Answer 7

Focus on the triangle AQC. we know its side AC = side BC of the other triangle

both have the same angle C
they told us angle CAQ= angle CBP

Answer 8

So AAS then....

Answer 9

you use the letters in the same order as the "parts"
notice that the side is sandwiched in between the two angles

Answer 10

ASA...got it!

Answer 11

once you prove the triangles are congruent you can say the corresponding sides
CQ and CP are congruent (Corresponding Parts of Congruent Triangles, or CPCT)

Answer 12

*CPCTC short for
Corresponding Parts of Congruent Triangles are Congruent

Answer 13

you say angle C in both triangles is congruent to itself because of the Reflexive Property

Answer 14

Okay. I've finished it. Thank you!