ABC is an isosceles triangle. BD is a median. Prove that 1) triangles ABD and CBD are right-angled

ABC is an isosceles triangle. BD is a median. Prove that 1) triangles ABD and CBD are right-angled 2) triangles ABD and CBD are equal.

We are given that BD is the median in the isosceles triangle given to us. Since it is known that in an isosceles triangle the median is also the height and the bisector, we can say that ВD is the height in the given isosceles triangle. Therefore, the angle ADC and the angle BDC are right angles, so triangles ABD and CBD are rectangular.

Consider triangles ABD and CBD, where AB = BC, BD is the common side, AD = DC (BD is the median in this triangle). Therefore triangles ABD and CBD are equal on three sides.