Question

if the bisector of the interior vertical angle of a triangle is parallel to the base. Show that triangle is isosceles.​

Answer 1

Answer:

Join A to D

Hence,

AD∥BC

⇒∠ACB=∠CAD(alternateangle)

⇒and∠BAC=∠ACD(alternateangle)

⇒

Hence

AB=AC (by ASA congurency )

so, it is isosceles triangle.

Answer 2

Join A to B

hence,

AD||BC

angle ACB =angle CAD ( alternate angle)

and angle BAC = angle ACB ( alternate angle)

Hence,

AB= AC ( by ASA congruency)

so, it is isosceles triangle.