The answer is (D).
HIDDEN SPECIAL TRIANGLES
It happens a lot that the key to solving a geometry problem is to add a line segment or two to the
figure. Often what results is one or more special triangles. The ability to spot, even to create, special
triangles comes in handy in a question like Example 4.
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.
Example 4
Figure 4
In Figure 4, the perimeter of isosceles trapezoid WXYZ is 62. If = 7 and = 25, what is
the length of diagonal WY?