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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.

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, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

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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