1972 AHSME Problems/Problem 18
Problem
Let be a trapezoid with the measure of base
twice that of base
, and let
be the point of intersection of the diagonals. If the measure of diagonal
is
, then that of segment
is equal to
Solution
We begin with a diagram:
The bases of a trapezoid are parallel by definition, so and
are alternate interior angles, and therefore equal. We have the same setup with
and
, meaning that
by AA Similarity. We could've also used the fact that
and
are vertical angles.
With this information, we can setup a ratio of corresponding sides:
And simplify from there:
Therefore, our answer is