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

QP¯¯¯¯¯¯¯¯
upper Q upper P

PT¯¯¯¯¯¯¯
upper P upper T

PR¯¯¯¯¯¯¯¯
upper P upper R
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Answer 1

In a parallelogram, opposite sides are congruent. Since \( QRST \) is a parallelogram, the segments \( QR \) and \( ST \) are congruent, and the segments \( QS \) and \( RT \) are also congruent. Additionally, the diagonals of a parallelogram bisect each other.

Since \( P \) is the intersection point of the diagonals \( QS \) and \( RT \), by the property of the bisection of the diagonals in a parallelogram, the segments \( SP \) and \( PT \) are congruent.

Therefore, the segment that must be congruent to segment \( SP \) is:

\( PT \) (upper P upper T).