Question

What additional information do you need to prove NOP=QSR?

Answer 1

After careful consideration i think I have an answer... 
So if you notice, These two triangles are a reflection of each other. 
Now even though these two triangles equal one another, we still have to consider the fact that they are different. (one side is the opposite of another)
So lets just name all the sides that equal each other. 
∠N = ∠Q
NO = QS
QR = NP
PO = SR
∠S = ∠O 
∠P = ∠R 

(by the way i'm going to be saying {the reflective side} every time i want to refer to the side with the two lines :P) - so bare with me. 

So therefore this would mean that ∠P = ∠S would be false, since one angle is from the side that is reflected and the other isn't. Makes sense?

So lets look over at the answers...

A.) PN = SQ 
For this answer choice, PN is on the non reflective side, while SQ is on the reflective side. Soooo... This answer choice is wrong. 

B.) NO = QR
NO  is part of the  unreflective side, while QR is part of the reflective side. 
Therefore this answer is wrong. They must be part of the same side. 

C.) ∠P = ∠S 
∠P is on the unreflective side, while angle ∠S is on the reflective side. 
There fore this answer is also wrong. 

D.) ∠O = ∠S 
Now ∠O is on the reflective side while ∠S is on the reflective as well. 
There fore this answer is correct . 

YOUR ANSWER IS. 
D.) ∠O = ∠S