Question

In the adjoining figure, AL and CM are perpendiculars to the diagonal BD of a || gm ABCD. Prove that (i) ∆ALD ≅ ∆CMB, (ii) AL = CM.

Answer 1

ABCD is a parallelogram.
∴ AD || BC and AD = BC
(i) In ∆ALD and ∆CMB, we have:
AD = BC
∠​ALD = ∠​CMB (90^o each)
∠​ADL = ∠​CBM (Alternate interior angle)
∴ ∆ALD ≅ ∆CMB

(ii) As ∆ALD ≅ ∆CMB (Proved above)
∴​ AL = CM (By CPCT)