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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.
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Solution
ABCD is a parallelogram in which ∠A and ∠C are obtuse.
Points X and Y are taken on the diagonal BD.
Such that ∠XAD = ∠YCB = 90°.
We need to prove that XA = YC
Proof:
ln ΔXAD and ΔYCB
∠XAD = ∠YCB= 90° ...[ Given ]
AD = BC ...[ Opposite sides of a parallelogram ]
∠ADX = ∠CBY ...[ Alternate angles ]
∴ By Angle-Side-Angle criterion of congruence,
ΔXAD ≅ ΔYCB
The corresponding parts of the congruent triangles are congruent.
∴ XA = YC ...[ c.p.c.t. ]
Hence proved.
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