Question

Which postulate or theorem can be used to prove that △PQR is similar to △PST?

Answer 1

I just took the test, it was SAS. 

Answer 2

Answer: SAS similarity theorem.

Step-by-step explanation:

In the given picture , we  have two triangles △PQR and △PST with common vertex P and common angle ∠P.

Also, the ratio of sides that include the common angle ∠P of ΔPQR and ΔPST is given by :-

$\frac{PS}{PQ}=\frac{45}{20}=\frac{9}{4}\\\\\frac{PT}{PR}=\frac{36}{16}=\frac{9}{4}$

Therefore, SAS similarity postulate ΔPQR is similar to ΔPST.

SAS similarity postulate says that if an angle of one triangle is equal to the corresponding angle of another triangle and the sides that include this angle are proportional, then the two triangles are similar.