D-derivative ABC. BE-median of this triangle ABC prove that BD is ABC-isosceles triangle. BD median. prove that

D-derivative ABC. BE-median of this triangle ABC prove that BD is ABC-isosceles triangle. BD median. prove that 1) the length of the segment BK 2) the degree measure of the angle BAK

Let’s start with a short entry given:

Triangle ABC,

BD is the median of the triangle,

∠ BDC = 90 °.

We need to prove that AB = BC.

We write down the equality: AD = DC by definition of the median.

Let’s prove it in two possible ways.

The first way.

It is known from the property of an isosceles triangle that the median in it is the height.

angle BDC = 90 °, which means that BD is the height, BD ⊥ АС,

triangle ABC is isosceles and therefore AB = BC.

Q.E.D.

Second way.

triangle ABD = triangle BDC, because BD is a common side, AD = DC, ∠ BDC = ∠ ADB.

We conclude from the equality of triangles that their similar sides are equal, AB = BC.

Q.E.D.