Question

please help me in solving this question​

Answer 1

Step-by-step explanation:

Let ABC be the triangle.

Given: AD bisects side BC

Hence BD = DC ...............(i)

Also given: It bisects angle A.

Hence Acc. to the basic proportionality theorem , we get—

AB/AC = BD/DC

=> AB /AC = BD/BD [ From (i) ]

=> AB = AC

Hence ABC is a triangle with two sides eq.

Therefore, ABC is isosceles

Hence proved

Thank you and keep smiling in this tough time

:)

Alternate solution

Since AD bisects BC, hence AD is median.

Also AD bisects Angle A

Hence AD is also the angle bisector of angle A .

Since the median and the angle bisector

are coinciding in the triangle

Hence it is also the perpendicular bisector of BC.

Hence, Angle ADB = ADC = 90⁰

Hence AB = AC

(Sides opp. to equal angles are equal)

Hence ABC is isosceles.

Therefore Proved ;)