Math, asked by singh6828, 1 year ago

plz give me answer in step by step 3 question class 9th​

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Answers

Answered by Anonymous
1

Given,

P, Q, R, S are the midpoints of AB, BC, CD and DA respectively.

ABCD is a rectangle

To Prove

PQRS is a rhombus.

Construction

Join AC.In ΔABC,

∴ PQ || AC and PQ = AC (Mid-point theorem) ... (1)

Similarly in ΔADC,

SR || AC and SR = AC (Mid-point theorem) ... (2)equ

PQ || SR and PQ = SR

in PQRS one pair of opposite side is parallel and equal

hence,PQRS is a parallelogram

∴ PS || QR and PS = QR (Opposite sides of parallelogram)... (3)

In ΔBCD, Q and R are the mid-points of side BC and CD respectively.

∴ QR || BD and QR =BD (Mid-point theorem) ... (4)

the diagonals of a rectangle are equal.

∴ AC = BD …(5)

By using equation (1), (2), (3), (4), and (5), we obtain

PQ = QR = SR = PS

, PQRS is a rhombus

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