Question

A,B,C and D are collinear points AB= CD and EAD us an isosceles triangle in which AE= ED show that EBC is also an isosceles triangle.

Answer 1

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Answer 2

In ∆AEB and ∆ECD

AE = ED (EAD is an isosceles triangle)

AB = CD (given)

angle A = angle D (AE = ED)

Now, ∆AEB is congruent to ∆ECD (by SAS)

By CPCT, BE = CE

Hence, ∆EBC is an isosceles triangle.