A#10 (due 2/5)

#71, 74a, 75, 79, 83

A#10 Handout (front)
A#10 Handout (back)

You may use the Two-Column Proof Tables template for #71, though it's only one problem. If not, make your own on your paper.

EDIT:

Answer Key

I'm not sure how to do 7-74and 7-83 b

Hi Nicki.

For 7-74 (I assume you mean part a), you can prove the triangles congruent by using the SAS congruency conjecture (the diagonal is congruent "to itself" in both triangles using the reflexive property, so both triangles are congruent that way). Because both triangles are congruent, then corresponding parts of the triangles are also congruent. The top and bottom sides are congruent to one another (as you can see), so the left and right sides also must be corresponding sides, and they must be congruent. Since they are, then:

6x + 6 = 8x + 2

You'll be able to solve for x then. Just make sure you understand the first part with CPCTC.

For 7-83, if you draw two triangles that are congruent, then its corresponding parts will also be congruent (just like the previous problem). So if triangle TAP is congruent to triangle DOG, then:

<T = <D
<A = <O
<P = <G

TA = DO
AP = OG
TP = DG

(check the post below for videos that explore CPCTC more)

Since TP = DG, and TP = 21 and DG = 2y + 7, then 2y + 7 = 21.

The important part of CPCTC-related problems is that the triangles must first be proven to be congruent before you can do anything else. Once they are, it opens a lot of doors for you to be able to do things with them.

Hope that helps!

CPCTC is explained in these three videos...


Check out 14:10 - 18:15 in this video:




Check out 32:28 - 37:04 in this video:




Then @ 28:15 - 36:15 we used CPCTC in a quadrilateral-related problem like the one you're doing now. Maybe it will help you here as well.