Question

In a triangle vertical angle bisector is a median of the triangle. Prove that triangle is isosceles.​

Answer 1

Step-by-step explanation:

given

angle BAD = angle CAD .......EQ 1

BD = CD

to prove = AB = AC

construction

DE = AD

now in triangle ABD and triangle CED

AD= DE ( by construction)

BD = CD ( given )

angle ADB = angle CDE ( vertical opposite angle)

by SAS criteria triangle ABD is congurent to triangle ECD

so by cpct

AB = CE

and angle BAD = angle CED ........EQ 2

from equation 1 and 2

angle CED = angle CAD

so

CA= CE

and

CE = AB ( proved above )

so

AC = AB