Question

If the bisector of the vertically angle of a triangle bisect the base,show that triangle is isosceles

Answer 1

Answer:

ΔABC is isosceles

Step-by-step explanation:

Let say ABC is the triangle

& AD ia angle bisector

BD = CD given

Produce AD to E such that AD=DE & then join E to C.

now in ΔABD & Δ ECD

∠ADB = ∠EDC opposite angles

BD = CD

AD=DE drawn

=> ΔABD ≅ Δ ECD

=> AB = CE

& ∠BAD = ∠CED

∠BAD = ∠CAD  = ∠BAC /2

=> ∠CED = ∠CAD

in ΔAEC

∠CED = ∠CAD

=> CE = AC

while AB = CE

=> AB = AC

=> ΔABC is isosceles