Question

in the given figure ab = AC prove that BD = BC ​

Answer 1

let angle CBD be x

AB = AC given

angle ACB = angle ABC

(since sides opposite to equal angles are equal)

In triangle ABC

angle abc + angle bac + angle cab = 180°

(30+x) + 40 + (30+x) = 180°

(since angle ACB = angle ABC proved above)

100 +2x = 180°

x = 40°

ANGLE CBD = 40°

In triangle ADB ,

angle ADB = 110° ( angle sum property of triangle)

angle BDC + angle ADB =180°(LINEAR PAIR)

Angle BDC = 70°

angle ADB = angle BCD + angle CBD (exterior angle property of triangle)

angle BCD = 70°

angle BCD = angle BDC

this shows that BC=BD

(since sides opposite to equal angles are equal)

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