# ​Solve this: Q6. In the adjoining figure, ABC is a triangle in which AD is the bisector of A. If AD$\perp$BC, show that $∆$ABC is isosceles.

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Dear Chesna,
Here is the prove:
To Prove: ​△ABC is an isosceles triangle.
To prove the above statement, we have to prove, AB = AC as opposite sides of isosceles triangle are equal.

So,

Now,

So, by the above mentioned factors, we can say that ADB ​≅ ADC by ASA congruency rule.

Now,
AB = AC {By C.P.C.T}

In an isosceles triangle the opposite sides should be equal.
Thus, △ ABC is an isoceles triangle.

Hope ithelps!
Thumbs up if it s is satisfactory!

Cheers!

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