Question

In the adjoining figure angle ABC=angle ACB, D and E are points on the sides AC and AB respectively such that BE = CD. Prove triangle EBC is congruent to triangle DCB

Answer 1

Given :  ∠ABC = ∠ACB ,   D and E are points on the sides AC and AB respectively such that BE = CD.

To find :   Prove triangle EBC is congruent to triangle DCB

Solution:

∠ABC = ∠ACB

D is on AC  &  E is on AB

=> ∠EBC = ∠DCB

in Δ EBC  & ΔDCB

BC =  BC   common

∠EBC = ∠DCB

BE  = CD   Given

=>  Δ EBC  ≅ ΔDCB   using SAS  rule

QED

Hence Proved

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Answer 2

Answer:

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