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Question

In the parallelogram ABCD, the angles A and C are obtuse. Points X and Y are taken on the diagonal BD such that the angles XAD and YCB are right angles.

Prove that: XA = YC.

State whether the above statement is true or false.


  1. True
  2. False

A
True
B
False
Solution
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In XAD and YCB
XAD=YCB (Given each 90)
AD=BC (Opposite sids of parallelogram are equal)
XDA=YBC (Alternate angles of parallel lines AD and BC)
XADYCB (ASA rule)
Thus, XA=YC (Corresponding sides)

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