Question

ABC is isosceles with AB=AC, AD is the altitude from A to side BC​,
prove that
(1) Traingle ADB is congruent to Traingle ADC
(2) Angle BAD= Angle CAD

Answer 1

Answer:

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Step-by-step explanation:

In tringle ABD & ACD

AB=AC (GIVEN)

ANGLE ADB=ANGLE ADC(BOTH ARE RIGHT ANGLES)

AD=AD(COMMON)

SO BOTH THE TRIANGLES ARE CONGRUENT

THEREFORE BD=CD(CPCT)

ANGLE BAD=ANGLE CAD(CPCT)

HENCE AD BISECTS BOTH BC AND ANGLE A

Answer 2

Step-by-step explanation:

In triangle ABD and ACD

AB=AC=(Given)

Angle ADB=Angle ADC (Both are right angles)

AD=AD (COMMON)

So,both the angles are congruent

Therefore BD=CD (CPCT)

Angle bad=Angle CAD (CPCT)

Hence AB bisects both BC and Angle A

Hope it helps!

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