Question

Prove that the bisector of the vertical
angle of an isosceles triangle bisects the
base at right angles.
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Answer 1

Answer:

let ABC be the triangle and AD be the bisector of angle A

Now we have 2 triangles ADB & ADC

therefore

AD=AD.............common sides

angle DAB = angle DAC...........given

AB =AC..............sides of isosceles triangle

hence ADB =ADC............SAS test ....1

now ,

angle ADB=angle ADC............from 1........2

and ADB+ADC=180..................linear pair

2ADB=180..............from 2

ADB=90

hence proved