Mathematics
In the adjoining figure, D is the midpoint of BC, DE and DF are perpendiculars to AB and AC respectively such that DE = DF. Prove that ABC is an isosceles triangle.
Triangles
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Answer
In △BED and △CFD,
∠BED = ∠CFD (Both are equal to 90°)
DE = DF (Given)
BD = DC (As D is the mid-point of BC.)
∴ △BED ≅ △CFD by RHS axiom.
We know that corresponding parts of congruent triangles are equal,
∴ ∠B = ∠C ⇒ AC = AB.
Hence, proved that ABC is an isosceles triangle.
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