Question

Triangles ACB and DFE are shown below.

Given: In ∆ACB, c2 = a2 + b2.
Prove: ∆ACB is a right angle.

Complete the flow chart proof with missing reasons to prove that ∆ACB is a right angle.

Which pair of reasons correctly completes this proof?

Answer 1

Wow, that's an overly complicated way of saying it's a right triangle because it satisfies Pythagorean Theorem.

Answer 2

Reason 1 substitution and reason 2 SAS

Answer 3

Here's a hint, though. in your given information you have two pairs of corresponding congruent sides, then along the way, you find a third pair of corresponding congruent sides.

Answer 4

@jsalemeh , it is not SAS because no angles were shown to be congruent.

Answer 5

It's bad enough when someone just gives an answer with no explanation; it's even worse when the answer is wrong... :-/

Answer 6

Can you figure it out from here @tornjeansxo ?

Answer 7

i'm so sorry i didn't reply, eek i had to leave the computer for a sec!

Answer 8

i'm sorry i'm still lost, haha @CliffSedge

Answer 9

I don't blame you. It is an overly-complicated and unnecessary proof.
What I mean is that in your initial information you have DF=AC and FE=CB by construction.
That is two pairs of congruent sides; then, between reasons 1&2 there is f=c, the third side.

Answer 10

i'm so so sorry i still haven't gotten this, i feel like such a bother. D: it's not B, but is it C?

Answer 11

Yes, it is definitely not B because that says "SAS" and I already explained why it isn't SAS.
Why do you think C is better?

Answer 12

well you said didn't say that substitution was wrong so i guessed :c

Answer 13

That's the trouble with these multiple choice proofs, if you get the answer by guess-and-check or process-of-elimination, then you don't really learn *why* the answers are correct.

Substitution is correct because it went from f^2 = d^2 + e^2 to f^2 = a^2 + b^2 after saying a=d and b=e.

Answer 14

oh! right right right i see now, thank you so much you've been helping me with questions all day hahah really i can't thank you enough!

Answer 15

You're welcome. These things can be tricky. Just take it slow and think through each step.