ABCD is a parallelogram, M is the mid-point
of BC and AM I BC. Prove that
AD2 = 4(CD2 - AM2)
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Given : ABCD is a parallelogram, M is the mid-point of BC and AM ⊥ BC
To Find : Prove that AD² = 4(CD² - AM²)
Solution:
Applying Pythagoras theorem as AM ⊥ BC
BM² = AB² - AM²
BM = BC/2 ( as M is mid point )
BC = AD ∵ opposite sides of parallelogram are equal
=> BM = AD/2
AB = CD ∵ opposite sides of parallelogram are equal
=> (AD/2)² = CD² - AM²
=> AD² / 4 = CD² - AM²
=> AD² = 4(CD² - AM²)
QED
Hence Proved
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