How do you prove the areas of the two triangles formed using the median of a triangle are congruent?

Answer 1

Vocabulary, kiddo. Shapes are congruent, but area is a number. Areas can be equal.

Since the median connects a vertex to the midpoint of the opposite side, turn the triangle so that side is the base and the vertex is at the top. The 2 triangles formed by the median have the same height since they have the same vertex, and they have equal bases (each 1/2 of the base of the whole triangle). So they have equal (not congruent) areas.

Answer 2

It's easy. Drop a perpendicular from the apex to the side of the triangle which is divided by the median. The median bisects that side, and the perpendicular defines the height of both triangles, and since the area is the base times the height, you'r done. (The areas are the same measure, not congruent.)

Answer 3

if the median of the first triangle is congruent then the stated area is congruent to the median