$In △ A B C, ∠ B = ∠ C . D and E are the mid points of AB and AC respectively. Then, the value of the ratio \frac{B E}{C D} is$ _______.

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Solution

The correct option is A
1

$Given, in △ A B C, ∠ B = ∠ C . D and E are the mid points of AB and AC respectively .$

$In △ A B E and △ A C D,$
$A B = A C$
(Sides opposite to equal angles of a triangle are equal.)
$⟹ A D = A E$
(halves of equal sides are equal)
$∠ A = ∠ A (common angle)$

$∴ △ A B E ≅ △ A C D$ (SAS rule)
$⟹ C D = B E$ (CPCTC)

$∴ \frac{B E}{C D} = 1$

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