In the adjoining figures, and are perpendiculars to the diagonal of a ||gm Prove that

Question

In the adjoining figures, and are perpendiculars to the diagonal of a ||gm Prove that (i) (ii)

Philoid · Accepted Answer

Here, ABCD is parallelogram.

Hence, 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 …from 1
∴ AL = CM …by cpct