+25 [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.
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.
