Here we look at the triangles on the legs of a trapezoid.

What’s going on: Given a trapezoid with diagonals, prove that the triangles on the legs have the same area.  (Even though the triangles are not congruent and not similar.)

Student handout: Triangles-in-a-Trapezoid-2

GeoGebra file: here

Teacher Notes

This is quite easy to show. Use the overlapping triangles with the base of segment AB. Remove the common triangle.

Important/Useful Takeaways for students:

  • Area of triangle is one-half times base times height. We’ll use this repeatedly and often. Do Draw In the height.
  • Triangles with the same base and same height (or congruent bases or congruent heights) have the same area.

In the next problem we will see a particularly significant relationship between the area of each of these triangles on the legs and the areas of the triangles on the bases.