Look at the figure.

triangle pts has measure of angle pts equal to 90 degrees. ris a point on the hypotenuse sp such that the segment rt is perpendicular to ps. q is a point outside the triangle on the left of r so that triangle pqr has the measure of angle pqr equal to 90 degrees

which pair of triangles is similar?
answer

triangles ptr and pqr

triangles rts and pqr

triangles pqr and pts

triangles srt and trp

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:

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