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Application of Similarity

In the adjoin...

Question

In the adjoining figure, $△ A B C$ is an isosceles triangle in which $A B = A C$ . If $E$ and $F$ be the midpoints of $A C$ and $A B$ respectively, prove that $B E = C F$ .

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Solution

$Δ A B C A B = A C ⟹ B F = E C ∠ B = ∠ C B C = B C$
By $S A S$ criteria
$Δ B F C \sim Δ C E B i m p l i e s B E = F C$

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