Question

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.​

Answer 1

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