Q. 44.3( 36 Votes )

# In the adjoining figure, the sides BA and CA have been produced such that BA = AD and CA = AE. Prove that DE || BC. [ hint:-use the concept of alternate angles.]

Answer :

In Δ AED and Δ ABC we have

BA = AD(Given)

CA = AE(Given)

∠EAD = ∠BAC (Vertically Opposite)

So Δ AED and Δ ABC are congruent by S.A.S. axiom of congruency

So we can say

∠AED = ∠ACB(Corresponding parts of Congruent triangles)

So ∠AED & ∠ACB forms a pair of alternate interior angles

Hence DE || BC

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