The side PQ of a parallelogram PQRS is produced to
T in such a way that QT = PQ. ST intersects QR at U.
The point U divides QR in the ratio.
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Answer:
U divides QR in 1 : 1 Ratio
Step-by-step explanation:
in Δ PST & Δ QUT
QU ║ PS as QR ║ PS & U lies on QR
Hence Angles
∠PST = ∠QUT & ∠SPT = ∠UQT
∠T is common
=> Δ PST ≈ Δ QUT
=> PT/QT = PS/QU
PT = PQ + QT = QT + QT = 2QT
=> 2QT/QT = PS/QU
=> PS = 2 * QU
PS = QR ( opposite sides of Parallelogram)
=> QR = 2 * QU
=> QU = QR/2
=> U divides QR in 1 : 1 Ratio
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