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.
In the adjoining figure,
AD ⊥ BC.
So,
∠ADC = 90°
∠ADB = 90° .... (1)
Now,
Lets take consider Triangles ADB and ADC,
In Triangles ADB and ADC,
∠BAD = ∠CAD {As ∠A is bisected}
AD = AD {Common side}
∠ADB = ∠ADC (=90°) {Using[1]}
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!
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Cheers!