Respuesta :

We have:

ab = bc (hypothetical)

so the triangle ABC is isosceles at B

we have: bd is the height of the triangle ABC, so BD is perpendicular to AB

Consider the triangle ABD and the right triangle ACD have:

AB = BC (hypothesis)

BD is the common edge

So the triangle ABD = triangle ACD (hypotenuse - acute angle)

hence the angle ABD = angle ACD