+0

# other problem (help convert asymptote as well)

0
15
1
+28

[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
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.