Prove that in an isosceles triangle, the height to the base divides the triangle into two equal triangles.

Given is an isosceles triangle ABC, angle A = C. Let’s draw the height BD, which will also be the median and bisector (since the triangle is isosceles). Received two triangles ABD and DBC, where side BD is common, AB = BC from the definition of an isosceles triangle and AD = DC, since the carried height BD, being also the median, divided the base of the speaker in half. Therefore, the triangle ABD \ DBC according to the third sign of equality of triangles, on three sides.