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SAS Criteria for Congruency of Triangles

If ∠ ADE = ...

Question

If $∠ A D E = ∠ A E D$ and $\frac{A D}{A B} = \frac{A E}{A C}$ , prove that $Δ B A C$ is an isosceles triangle.

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Solution

$\frac{A D}{A B} = \frac{A E}{A C}$

$\Rightarrow A B = A C$

$∠ A D E = ∠ A E D$

$\Rightarrow ∠ A B C = ∠ A C B$

Since 2 sides are congruent, and

2 angles are congruent.

Given triangle is an Isosceles triangle.

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