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AAS Criteria for Congruency

In triangle A...

Question

In triangle ABC, altitudes BE and CF are equal. Prove that the triangle is isosceles.

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Solution

In ΔABE and Δ ACF,
∠A = ∠A[Common]
∠AEB = ∠AFC = 90° [Given: BE AC; CF AB]
BE = CF [Given]
Δ ABE ≅ Δ ACF (AAS)
So AB=AC (Corresponding parts of Congruent Triangles)
Since two sides of triangle are equal,
Therefore, ABC is an isosceles triangle.

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