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.

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

PT¯¯¯¯¯¯¯
upper P upper T

QP¯¯¯¯¯¯¯¯
upper Q upper P

PR¯¯¯¯¯¯¯¯
upper P upper R

QS¯¯¯¯¯¯¯

GPT-4o mini · Answer

In a parallelogram, the diagonals bisect each other. Given that QRST is a parallelogram and that P is the intersection point of the diagonals, it follows that segments SP and PT are congruent.

Since we want to find the segment that is congruent to segment SP, the correct response is:

PT