ADD TO THE FIGURE
Often the breakthrough on a plane geometry problem comes when
you add a line segment or two to the figure. Perpendiculars can be
especially useful. They can function as rectangle sides or triangle
altitudes or right triangle legs.There aren’t any special triangles yet. As so often happens, though, you can
get some by constructing altitudes. Drop perpendiculars from points B and C,
and you make two right triangles. The length 21 of side then gets split
into 6, 9, and 6.
Now you can see that those right triangles are 3-4-5s (times 2) and that the
height of the trapezoid is 8. Now look at the right triangle of which is the
hypotenuse.