Question

Supply the missing reasons to complete the proof:

Answer 1

Since you are proving triangles congruent, you have to use a theorem, like SSS AAS ASA etc.... and looking at what is given and the fact the line before was vertical angles... which one do you think we will use?

Answer 2

I have no clue. Proofs literally stress me out to no end.

Answer 3

okay... well if you look at the given statement... the first piece says that Q and T are congruent... that is one angle of one triangle and one angle of another triangle... do you see that?

Answer 4

yes!

Answer 5

okay, then the next part of the given says QR and TR are congruent... that is one side of one triangle and one side of another triangle are congruent as well...

so the given statement tells use that a set of ANGLES are congruent and a set of SIDES are congruent....

the next lines tells use that another set of ANGLES are congruent because of the vertical angle thing....

so now in all we have sets of ANGLES, SIDES, and ANGLES all congruent... do you see that??

Answer 6

yeppp

Answer 7

great... so the theorem that we would use to prove that the triangles are congruent... is

ASA.... which stands for exactly what we just found, angle side angle...and that is what goes in the first blank

Answer 8

okay... so how do we find out the last one?

Answer 9

well the last one is just proving PARTS of triangles are congruent... and anytime you prove parts of triangles you use CPCTC... which stands for Congruent Parts of Congruent Triangles are Congruent

Answer 10

so that's what put? CPCTC?

Answer 11

yup thats it