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Question

The figure shows a parallelogram PQRS, in which, A is the mid point of PQ and B is the mid point of RS.

Statement 1: SX=XY

Statement 2: XY=QY


A

S1 is true but S2 is false

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B

S1 is false but S2 is true

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C

S1 and S2 are both true

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D

S1 and S2 are both false

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Solution

The correct option is C

S1 and S2 are both true


As, B is the mid point of RSBR=12RS

Also, A is the mid point of PQAP=12PQ

PQRS is a parallelogram, so that,
PQ=RS and PQRS

Therefore, BR=AP and BRAP

Thus, PARB is a parallelogram PBAR

In SYR, by converse of mid point theorem X is the mid point of SYSX=XY

In QPX, by converse of mid point theorem Y is the mid point of QXQY=XY

Therefore, both Statement 1 and Statement 2 are true.


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