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
PR¯¯¯¯¯¯¯¯
upper P upper R
QP¯¯¯¯¯¯¯¯
upper Q upper P
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1 answer
In a parallelogram, the diagonals bisect each other. This means that the segments created by the diagonals, when they intersect at point P, are congruent.
Since SP is one of the segments formed by one of the diagonals (QS and RT), the segment that must be congruent to segment SP is segment PT.
Therefore, the correct response is:
PT¯¯¯¯¯¯¯ upper P upper T
