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AAS Criteria for Congruency

In an isoscel...

Question

In an isosceles triangle $A B C$ , $A B = A C . D$ and $E$ are points on $B C$ such that $B E = C D .$ Calculate the value of $\frac{A D}{A E}$ .

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Solution

In $△ A B D$ and $△ A C E,$

$A B = A C$ [given]

$∠ B = ∠ C$ [angles opposite to equal sides]

$B E = C D$ [Given]

Subtracting $D E$ from both sides, we get

$B E - D E = C D - D E$

$B D = C E$

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

Therefore, $A D = A E$ [Corresponding parts of congruent triangles are congruent]

$\Rightarrow \frac{A D}{A E} = 1$

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