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SAS Criteria for Congruency

In an isoscel...

Question

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD. The value of $\frac{A D}{A E}$ is equal to

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Solution

The correct option is A 1
$In △ A B D and △ A C E,$
$A B = A C (given)$ --- (i)
$∠ B = ∠ C$ --- (ii)
[ $∵$ AB = AC (given) and angles opposite to equal sides of a triangle are equal.]
$Given, B E = C D$
$⟹ (B E - D E) = (C D - D E)$
$⟹ B D = C E$ --- (iii)
$∴ △ A B D ≅ △ A C E$ (SAS congruency)
$⟹ A D = A E (C P C T)$
$⟹ \frac{A D}{A E} = 1$

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