Characterization of a Trapezoid (US) / Trapezium (UK)
- Linda Fahlberg-Stojanovska
The sides a and b are parallel. Click and drag any of the outside vertices. Notice that the blue and red triangles formed by the diagonals always have the same area. Notice that the green and orange triangles are always similar. Notice that the line segment joining the midpoints of the parallel sides always passes through the intersection point of the diagonals. Each of these properties is a characterization that the quadrilateral is a trapezoid (US)/ trapezium (UK).
Why are the inside angles of each non-parallel side supplementary (add up to 180 degrees)? Can you notice that the ratio of the parts of the line segment joining the midpoints is the same as the ratio between the lengths of the parallel sides? Isn't that cool?