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.