Question

Look at the figure.

Answer 1

Answer:ΔSRT and ΔTRP

Step-by-step explanation:

We are given that R is a point on hypotenuse SP such that the segment RT is perpendicular to PS, therefore, PR=RS as the perpendicular bisector divides the line segment in two equal halves.

Now,

In ΔSRT and ΔTRP,

PR=SR( Since RT is perpendicular bisector, it divides PS in two equal halves)

∠PRT=∠SRT=90° (RT is perpendicular bisector of PS)

RT=RT(Common)

Therefore, by SAS rule of congruency,

ΔSRT ≅ΔTRP

Hence, Option D is correct.

Answer 2

I believe the correct answer from the choices listed above is the third option. The pair of triangles that are similar are the triangles PQR and PTS. They both are isosceles triangles with the same ratio of the corresponding lengths. Hope this answers the question. Have a nice day.