BE and CF are two Equal altitudes of a triangle ABC. using RHS congruence rule , prove that the triangle ABC is isosceles
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Consider triangle BFC AND CEB
BC = CB. ( COMMON )
ANGLE BFC = ANGLE CEB = 90 (GIVEN)
CF = BE. ( GIVEN )
SO, triangle BFC is congruent to triangle CEB. ( RHS )
Hence , BF = CE. ( CPCT )_____________(1)
and, considered triangle ABE and ACF
angle BAC = angle CAB. ( COMMON )
angle AFC = angle AEB. (GIVEN)
CF = BE. (GIVEN)
HENCE,. triangle ABE is congruent to triangle ACF. (AAS)
So, AF = AE. (CPCT). _______________(2)
adding (1) and (2)
we get,
BF + AF = CE + AE
AB = AC
hence , triangle ABC is iso. triangle.
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