To prove that the diagonals of rectangle q r p n are congruent, c p c t c can be used after proving which statement? a. triangle p n q is congruent to triangle n p r by the s a s congruence postulate. b. triangle n q r is congruent to triangle r p n by the s s s congruence postulate. c. triangle q r p is congruent to triangle p n q by the h l congruence theorem. d. triangle q r p is congruent to triangle p n q by the s s s congruence postulate.

A. triangle P N Q is congruent to triangle N P R by the S A S Congruence Postulate. Let's take a look at the options and determine which make sense and which doesn't. A. triangle P N Q is congruent to triangle N P R by the S A S Congruence Postulate. * This is true. You have a side, a 90 degree angle, and another side. So this is the correct choice. B. triangle N Q R is congruent to triangle R P N by the S S S Congruence Postulate. * The problem with this choice is although two triangles are congruent due to the SSS postulate, it's assuming that the diagonals are already congruent. And since our objective is to prove that they're congruent, basing your proof upon their already being congruent is faulty. So this is a bad choice. C. triangle Q R P is congruent to triangle P N Q by the H L Congruence Theorem. * The H L Congruence Theorem is true here as well. But it's still assuming that the diagonals (aka the hypotenuse of the right triangle in the H L Congruence Theorem) to already be congruent which is what we're attempting to prove. So this too is a bad choice. D. triangle Q R P is congruent to triangle P N Q by the S S S Congruence Postulate. * This is a bad choice for the same reason as option "C" above. Assuming the results of your proof to be true prior to proving it is a bad idea. So this is a bad choice. Overall, only open "A" works. All of options "B" through "D" assume the congruence of the diagonals prior to actually proving that they're congruent. It's like trying to win an argument with someone by stating "I'll prove that I'm right. Because I'm right, therefore I'm right." Doesn't make a whole lot of logical sense, does it? But that's exactly what "B" through "D" are doing.