Question

In ∆ABC, AD is perpendicular to BC and AD bisects A. Prove that ∆ ABD is
congruent to ∆ ACD. Also, prove that ∆ ABC is isosceles.

Answer 1

Answer:

In triangle ABD and triangle ACD

Angle BAD = Angle CAD (Given)

AD = AD ( Common)

Angle BDA = Angle CDA (Each 90 degree)

Therefore, triangle ABD is congruent to triangle ACD ( by ASA)

Hence, AB = AC ( by CPCT)

Since, AB = AC

Therefore, triangle ABC is isosceles triangle (Two sides of isosceles triangle are equal)

Hope it helped you.....

Answer 2

Answer:

In triangle ADB and triangle ADC

Angle ADB= Angle ADC (90°)

AD=AD (common)

Angle ABD= Angle ACD (Given)

Triangle ADB is congrunt to triangle ADC (ASA)

AB=AC (CPCT)

Hence proved

Step-by-step explanation:

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