Mathematics
ABCD is a parallelogram in which ∠A and ∠C are obtuse. Points X and Y are taken on diagonal BD such that ∠AXD = ∠CYB = 90°. Prove that : XA = YC.
Triangles
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Answer
AD || BC and BD is the transversal.
⇒ ∠ADX = ∠CBY (Alternate interior angles are equal)
In △XAD and △YCB,
⇒ ∠ADX = ∠CBY (Proved above)
⇒ ∠AXD = ∠BYC (Both equal to 90°)
⇒ AD = BC (Opposite sides of a parallelogram are equal)
∴ △XAD ≅ △YCB (By A.A.S. axiom)
⇒ XA = YC (Corresponding parts of congruent triangles are equal)
Hence, proved that XA = YC.
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