Question

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD Show that AD = AE​

Answer 1

Step-by-step explanation:

In Triangle ABE and Triangle ADC,

AB=AC. (Given)

BE=CD. (Given)

<B=<C. (property of an isosceles triangle)

Triangle ABE is congruent to Triangle ADC.

AD=AE. (C.P.CT) answer.

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Answer 2

Step-by-step explanation:                                                                          

In Δ ABD and Δ ACE,

AB=AC       [given] {1}

∠B=∠C

[Angles opposite to equal sides] {2}

Also,       BE=CD

So,          BE - DE = CD - DE

That is,   BD = CE {3}

So,          Δ ABD ≅ ΔACE

[Using {1}, {2}, {3} and SAS rule].

This gives,   AD = AE [CPCT]

NOTE :- CPCT= Corresponding parts of congruent triangles.

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