Question

Determine whether each pair of triangles is similar. Justify your answer.

S

18
00
R
9
P
16
T
yes; AQRP ~ ASRT by SAS Similarity
yes; AQRP ~ ATRS by SAS Similarity
yes; AQRP - ATRS by ASA Similarity
No; The corresponding sides are not proportional.

Answer 1

Option (2)

Explanation:

By the theorem (SAS) of similarity,

"If two sides of one triangle are proportional to the corresponding sides of another triangle and the included angles in both the triangles are equal then both the triangles are similar."

It's given in the figure attached,

`(QR)/(TR)=(PR)/(RS)`

`(8)/(16)=(9)/(18)`

`(1)/(2)=(1)/(2)`

And m∠QRP ≅ m∠TRS

Therefore, corresponding sides of ΔQRP and ΔTRS will be similar.

Option (2) will be the answer.