Answer:
D.
Step-by-step explanation:
There is nothing in the figure to indicate the triangles are isosceles. This eliminates answer choices A, B, C.
Answer choice D is a required step in the proof, but only gets part of the way. The triangle similarity means ...
SQ/PQ = TQ/RQ
From here, you need to decompose each of the sides PQ and RQ into parts. Then you can get to the desired relationship.
(PQ -PS)/PQ = (RQ -RT)/RQ . . . segment sum theorem
1 - PS/PQ = 1 -RT/RQ . . . . . . . do the division
-PS/PQ = -RT/RQ . . . . . . . . subtract 1 (subtraction property of equality)
PS/PQ = RT/RQ . . . . . . . . multiply by -1 (multiplication property of equality)
