Question

D is the mid point of BC ansd perpendicular DF and DE to sides AB and AC respectively are equal in length. prove that triangle ABC is an isosceles triangle .​

Answer 1

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Answer 2

If ABC is a triangle and D is a midpoint of BC, and the perpendiculars from D to AB and AC are equal, how do you prove that the triangle is isosceles?







In triangles BED and CFD ,

BD= DC ( Dis the midpoint)

DE = DF ( given)

Angles BED and CFD are both right angles.

Hence the triangles are congurent by RHS condition.

Thus angles B and C are equal by c.p.c.t

thus AB = AC ( sides oppposite to equal angles of a triangle are equal).