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Question -

ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that тИЖABC is an isosceles.



Answer -

Given : In тИЖABC,
BE тКе AC and CF тКе AB
BE = CF
┬а
To prove : AABC is an isosceles triangle
Proof : In right ABCE and ABCF Side
BE = CF (Given)
Hyp. BC = BC (Common)
тИ┤ тИЖBCE тЙЕ тИЖBCF (RHS axiom)
тИ┤ тИаBCE = тИаCBF (c.p.c.t.)
тИ┤ AB = AC (Sides opposite to equal angles)
тИ┤ тИЖABC is an isosceles triangle

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