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

PR¯¯¯¯¯¯¯¯
upper P upper R

QS¯¯¯¯¯¯¯
upper Q upper S

PT¯¯¯¯¯¯¯
upper P upper T

QP¯¯¯¯¯¯¯¯

Answer 1

In a parallelogram, the diagonals bisect each other. This means that the segments formed by the intersection of the diagonals are congruent.

Given that segment \( SP \) is one part of diagonal \( QS \) that connects vertices \( Q \) and \( S \), the segment that must be congruent to \( SP \) is the part of the diagonal \( PR \), which is the other segment created by the intersection of the diagonals \( QT \) and \( SR \).

Thus, the segment of the figure that must be congruent to segment \( SP \) is \( PR \).

Final answer: **PR**