[asy]

size(5cm);

pair P = (0,0);

pair Q = (2.1,1);

pair R = (1.9,-1);

pair ptS = (3,0);

draw(P--Q--ptS--R--cycle);

draw(P--ptS);

label("$P$",P,W);

label("$Q$",Q,N);

label("$R$",R,S);

label("$S$",ptS,SE);

[/asy]

idk how to get it on here so for anyone who is able to please do it

here is the problem:

In the figure above, \(\overline {PS}\) bisects \(\angle QPR\). We can ensure that \(\triangle PQS\cong\triangle PRS\) by adding just one more condition. Which of the following statements could be that condition?

A) \(PQ=PR\)

B) \(SQ=SR\)

C) \(\angle PQS =\angle PRS\)

D) \(\angle PSQ =\angle PSR\)

There may be more than one possible statement. If there is more than one, type your answer as a list of letters separated by commas.

chippers44 Sep 9, 2023

#1**0 **

We are given that PS bisects ∠QPR, so ∠PSQ=∠PSR.

If we add the condition that PQ=PR, then we have SAS congruence, so △PQS≅△PRS.

The other conditions are not enough to guarantee congruence. For example, if SQ=SR, then △PQS and △PRS are similar, but not congruent.

Therefore, the answer is A.

Guest Sep 9, 2023