Question

In triangle ABC,AD is the angles bisector of angle A such that AD is
perpendicular to BC . Prove that triangle ABC is an isosceles triangle.

​

Answer 1

Refer to the above attachment.

Answer 2

$\huge{\underline{\underline{\mathbb{Given}}}}$

• Line AD is perpendicular to BC i.e angle ADB = angle ADC = 90°
• AD is bisector of Angle A also . Angle DAB = Angle DAC .

$\huge{\underline{\underline{\mathbb{To\:Prove}}}}$

Triangle ABC is an isosceles triangle i.e AB = AC .

$\huge{\underline{\underline{\mathbb{Proof}}}}$

In ∆ ABD and ∆ ADC

Angle ADB = Angle ADC (90°)

Angle DAB = Angle DAC (given)

AD = AD (common )

∆ABD ≈ ∆ADC { ≈ refers to congurent }

By ASA criteria .

.°. AB = AC { By C.P.C.T }

Hence proved