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
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.