Question

In the figure if AD=BD=CD PROVE THAT ANGLE BAC IS RIGHT ANGLE

Answer 1

Where is the figure?

Answer 2

Let angle DAB= Angle 1
Angle DBA= Angle 2
Angle DAC= Angle 3
Angle DCA= Angle 4

Angle 1 = Angle 2 (Angles opp. To equal angles are equal) ....(1)
Similarly
Angle 3 = Angle 4 ....(2)

Adding (1) and (2)

Angle 1 + Angle 3 = Angle 2 + Angle 4 ....(3)

Let Angle 1 + Angle 3 = Angle 5 ....(4)

Therefore Angle 5 + Angle 4 + Angle 2 = 180

Substituting values of the above equation from (3) and (4)

Angle 1 + Angle 2 + Angle 1 + Angle 2 = 180

2(Angle 1 + Angle 2) = 180

Angle 1 + Angle 2 = 180

Angle BAC = 90

Hence proved