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

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Solution

In $△ A B E$ and $△ A C D,$

$A B = A C$ ... (i) [opposite sides of equal angles]

$∠ A = ∠ A$ [common angle]

$A D = A E$ [halves of equal sides from (i)]

$\Rightarrow △ A B E ≅ △ A C D$ [SAS rule]

$\Rightarrow C D = B E$ [Corresponding parts of congruent triangles are congruent]

Hence, $\frac{B E}{C D} = 1$

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

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△

△

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