Question

If the bisector of exterior vertical angle of a triangle be parallel to the base , show that the triangle is isosceles

Answer 1

∠CAE is the external vertical angle and AD is its bisector. ∴ ∠CAD = ∠DAE ...... (i) As, AD || BC ∴ ∠CAD = ∠ACB ...... (ii) (alternate angle) and ∠DAE = ∠ABC ......(iii) (corresponding angle) From (i), (ii) and (iii), ∠ABC = ∠ACB ∴ AC = AB (opposite sides to equal angles) Hence, ΔABC is isosceles.