Question

Given PQ | | ST.

Triangle P Q R. Side P Q is 8 centimeters and side P R is 12 centimeters. Triangle S R T. Side S T is x centimeters and side R T is 18 centimeters.

Which statement is true based on the diagram?
TrianglePQR ~ TriangleSTR
TriangleRST ~ TriangleRQP
QR corresponds to TR.
PR corresponds to RS.

Answer 1

PQ ∥ ST ⇒ corresponding angles give the similarity P ↔ S, Q ↔ T, R ↔ R.
So:
- Triangle PQR ~ Triangle STR — true.
- Triangle RST ~ Triangle RQP — false.
- QR corresponds to TR — true.
- PR corresponds to RS — true.