Question

triangle ABC is an isosceles right angled at A and AL bisects BC. prove that angle BAL= angle ACD

Answer 1

here is your answer OK

.........We will use the SSS congruency rule to prove this.

In ∆ABD and ∆ACD,

AB=AC (given)

AD=AD (common)

BD=CD (given AD is the bisector)

So, ∆ABD is congruent to ∆ACD on SSS rule.

By CPCT, angle ADB = angle ADC

But BDC is a straight line, so angle ADB+angle ADC = 180°

Which implies angle ADB=90°

Hence proved.