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Question -

BE and CF are two equal altitudes of atriangle ABC. Using RHS congruence rule, prove that the triangle ABC isisosceles.



Answer -

In ╬ФBEC and ╬ФCFB,

тИаBEC = тИаCFB (Each 90┬░)

BC = CB (Common)

BE = CF (Given)

тИ┤ ╬ФBEC тЙЕ ╬ФCFB (By RHS congruency)

тЗТ тИаBCE = тИаCBF (By CPCT)

тИ┤ AB = AC (Sides opposite to equal angles of a triangle areequal)

Hence, ╬ФABC is isosceles.

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