Triangle_Area

Suppose ΔABC and ΔABD share the same base, AB, and the line through C,D is parallel to AB.

We can see the the two triangles have the same area.
Try dragging different vertices around and see what happens.

Why do these two triangles have the same area no matter where we drag the vertices.

As long as the line through C,D is parallel to AB, then the two triangles will have the same height, with that height being the distance between the parallel lines. Also, since they share the same base we will always get the same value when we apply the triangle area formula.

Teresa Munninghoff, Created with GeoGebra