## Geometry: Common Core (15th Edition)

Two angles in one triangle are congruent to two angles in the other triangle, so the triangles are similar according to the AA Similarity Postulate. $x = 180$ ft.
These two triangles are similar because two angles are congruent, so they are similar according to the AA Similarity Postulate. One angle in each triangle is a right angle, and right angles are congruent. Two angles are vertical angles; therefore, these angles are congruent because vertical angles are congruent. If two triangles are similar, then their sides are proportional. Let's find the scale factor for a pair of sides first: $\frac{90}{135}$ Divide both the numerator and denominator by their greatest common factor, $45$: $\frac{2}{3}$ This gives: $\frac{120}{x} = \frac{2}{3}$ Cross multiply to get rid of fractions: $2x = 360$ Divide each side by $2$ to solve for $x$: $x = 180$ ft.