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[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.

 Sep 9, 2023
 #1
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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​.

 Sep 9, 2023

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