Question

Hello, so I have this one other question. It's the last one. I actually worked out y, and I also worked out z and x but I'm not sure those are right. My teacher asked me to show my work. I hadn't shown my work because I thought that since the triangles were congruent, and they are supposed to measure 180, then it was pretty given that z= 109 and that x=33. However, I'm trying to see if that is right and if so, how can I "show my work" when it makes sense. if it isn't right, then please help me solve this. I will attach the image now.

Answer 1

Ok first of all you're absolutely right, to prove this you could 1) parallel lines (think of Alternate interior or 2) (If you've learned about this yet) CPCTC

Answer 2

CPCTC= Corresponding Parts of Congruent Triangles are Congruent

Answer 3

That's what I thought. So you are saying to justify z being 109, I can say it is 109 because Alternate Interior Angles are congruent?

Answer 4

Well not exactly, you can say that x= 33 degrees through alternate interior and then afterwards find y

Answer 5

After you find y, you know y =

Answer 6

The angle higlighted is also = to y through alternate interior

Answer 7

then you can find z by taking the degrees in a triangle and subtracting the angle higlighted above and x from it

Answer 8

I know what y is, it is 38

Answer 9

so if y is 38, then must also be 38 right

Answer 10

Hold on, I'm a bit lost

Answer 11

Ok, tell me where you lost me

Answer 12

Oh okay, so you are saying because y is 38, then that angle up there, which is not truly named in the picture is also 38?

Answer 13

Yep, using the same reasoning as the x=33, the alternate interior angle theorem

Answer 14

Oh okay, so now, to find x, it would be 180 - 38 +109

Answer 15

Well you already know x, it's 33, we established that earlier remember,
through Alternate Interior angle, because the lines are parallel

Answer 16

Right now we are trying to prove what z equals

Answer 17

I mean yeah I know that, but since I have to explain it. I just want to be clear! :) Wait, isn't z = 109, because the alternate interior angles are equal? That's why I put 109 there

Answer 18

z is 109 but you can't prove it through alternate interior angles

Answer 19

You can only prove x and y through alternate interior

Answer 20

How come?

Answer 21

because look