Triangles!!!

[tinalovesyou]

I was thinking i could prove it by using the side-side-side postulate, but in order to do that, I would need to be able to say that PS is congruent to QP, QR, or RS. Is there any way i could prove that PS is congruent to these, or should i go about it a different way?
(btw, we already proved that triangle RUQ is congruent to triangle RUS, and that triangle QTP is congruent to triangle QTS)

 

[Dr.Peterson]

View attachment 23802
I was thinking i could prove it by using the side-side-side postulate, but in order to do that, I would need to be able to say that PS is congruent to QP, QR, or RS. Is there any way i could prove that PS is congruent to these, or should i go about it a different way?
(btw, we already proved that triangle RUQ is congruent to triangle RUS, and that triangle QTP is congruent to triangle QTS)

Thanks for telling about your thinking, and about what the "two previous proofs" are!

Note that it asks you to prove that QPS and RQS are congruent; the order of vertices matters, so if you use SSS, you will need specifically to show that PS is congruent to QS, not one of the others. Do you see that?

You should also mark up sides (and maybe angles) to show what is implied by the two known congruences. In particular, you can put another single hash mark on a side, and another double hash mark that will be harder to show, but you should be aware of it.

Then you should have all the pieces you need.