Question

In an isosceles triangle ABC with AB= AC, D and E are two points on BC such that BE= CD. Show that ∆ ADE is an isosceles triangle.

Answer 1

$\star{\underline{\underline{\sf\purple{ Solution:-} }}}$

In ∆ABD and ∆ ACE,

• AB = AC ( Given 1)

• ∠B = ∠ C ( Opposite equal side ) (...2)

Also,

BE = CD

So,

[ BE - DE = CD - DE ]

That it,

BD = CE ( .......3)

So,

∆ ABD ≅ ∆ACE

( using (1) , (2) , (3) and SAS rule)

Hence,

This proves ∆ADE that is an isosceles triangle.

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Thanks