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
QP¯¯¯¯¯¯¯¯
upper Q upper P
QS¯¯¯¯¯¯¯
upper Q upper S
PT¯¯¯¯¯¯¯
upper P upper T
PR¯¯¯¯¯¯¯¯
1 answer
In a parallelogram, the diagonals bisect each other. This means that each diagonal divides the parallelogram into two equal segments at their intersection point.
Since \( P \) is the point of intersection of the diagonals \( QT \) and \( RS \), the segments \( SP \) and \( PR \) will be congruent because they are both half of diagonal \( RS \). Therefore, the segment that must be congruent to segment \( SP \) is:
PR
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