Q. 2
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE=CF, prove that ΔABC is isosceles.
Answer :
Given that ABC is a triangle in which BE and CF are perpendiculars to the side AC and AB respectively.
Such that,
BE = CF
We have to prove that, 
is isosceles triangle.
Now, consider 
We have,
∠BFC = ∠CEB = 90o (Given)
BC = CB (Given)
CF = BE (Given)
So, by RHS congruence rule, we have
∠FBC = ∠ECB (By c.p.c.t)
∠ABC = ∠ACB (By c.p.c.t)
AC = AB (Opposite sides of equal angles are equal in a triangle)
Therefore, 
is isosceles.
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