Question

In the drawing below, Side P Q is parallel to Side S T. Triangle PQR is similar to triangle TSR.

Lines P Q and S T are parallel. Triangles P Q R and T S R are similar.

Which statement about the sides is true?
Side Q R corresponds to Side R T.
Side P R corresponds to Side T R.
Side S R corresponds to Side P R.
Side S T corresponds to Side P T.

Answers

Answered by GPT-4o mini
In similar triangles, corresponding sides are proportional and correspond to one another based on their position in the triangles. Given that triangles PQR and TSR are similar, we can determine the corresponding sides based on their vertices.

1. The vertices of triangle PQR suggest that:
- P corresponds to T
- Q corresponds to S
- R corresponds to R (the vertex that is common to both triangles)

Using this correspondence, we can analyze the statements one by one:

- **Side Q R corresponds to Side R T.**
This statement is false. Side QR corresponds to TR.

- **Side P R corresponds to Side T R.**
This statement is correct. Side PR corresponds to side TR.

- **Side S R corresponds to Side P R.**
This statement is false. Side SR corresponds to side PQ.

- **Side S T corresponds to Side P Q.**
This statement is true based on the fact that lines PQ and ST are parallel, and thus they correspond.

Based on these evaluations, the true statements regarding the sides are:

- **Side P R corresponds to Side T R.**
- **Side S T corresponds to Side P Q.**

Therefore, the most direct and correct answer regarding side correspondence from the given statements is:

**Side P R corresponds to Side T R.**

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