1972 AHSME Problems/Problem 18
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
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