Question

Question

Use the image to answer the question.

A parallelogram has vertices upper Q, upper R, upper S, and upper T. Opposite vertices are connected via diagonal lines that intersect at an interior point labeled upper P. Sides upper Q upper R and upper T upper S are much longer than the other sides.

It is given that quadrilateral QRST
is a parallelogram. Which segment of the figure must be congruent to segment SP¯¯¯¯¯¯¯
?

(1 point)
Responses

QS¯¯¯¯¯¯¯
upper Q upper S

PT¯¯¯¯¯¯¯
upper P upper T

QP¯¯¯¯¯¯¯¯
upper Q upper P

PR¯¯¯¯¯¯¯¯
upper P upper R
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Answer 1

In a parallelogram, opposite sides are congruent. Given that QRST is a parallelogram, we can conclude the following:

• The sides QR and TS are congruent.
• The sides QS and RT are congruent.

Since segments SP and PT intersect at point P, segment SP is part of the diagonal RS, and segment PT is part of the diagonal QT.

To find a segment that must be congruent to segment SP, we can look at the other diagonal segments. Since diagonals bisect each other in a parallelogram, we know that:

• PS is congruent to PR (because both segments are half of the same diagonal RS).

Therefore:

• Segment PR (from point P to point R) is congruent to segment SP.

The correct response to your question is:

PR¯¯¯¯¯¯¯¯ (upper P upper R).