Question

Prove that the bisectors of the base angles of an isosceles triangle are equal.

Answer 1

In ΔABC,
AB = AC                 ....[ Given ]
∴ ∠C = ∠B             ......(i) [ Angles opp. to equal sides are equal]

⇒ `1/2∠"C" = 1/2` ∠B

⇒ ∠BCF = ∠CBE       ...(ii)

In ΔBCE and ΔCBF,
∠C = ∠B                 ...[ From (i) ]
∠BCF = ∠CBE         ...[ From (ii) ]
BC = BC                 ...[ Common ]
∴ ΔBCE ≅ ΔCBF     ...[ AAS ]
⇒ BE = CF              ...[ c. p.c.t ]