## Geometry: Common Core (15th Edition)

$x = 8$ $y = 9$ $z = 5.25$
Similar polygons have congruent angles and proportional sides. If these two quadrilaterals are similar, we would expect the sides to be similar. We are given definite values for similar sides in the two quadrilaterals, so let us find the scale factor for the two quadrilaterals: scale factor = $\frac{9}{6}$ Divide both the numerator and denominator by their greatest common factor, $3$, to simplify: scale factor = $\frac{3}{2}$ Now we can use this scale factor to set up proportions for the other sides to find the values of $x$, $y$, and $z$. Let's set up the proportion to find $x$ first: $\frac{12}{x} = \frac{3}{2}$ Get rid of the fractions by using the cross products property to multiply the numerator of one fraction with the denominator of the other fraction, and vice versa: $3x = 24$ Divide each side by $3$ to solve for $x$: $x = 8$ Now, let's set up the proportion to find $y$: $\frac{y}{6} = \frac{3}{2}$ Get rid of the fractions by using the cross products property to multiply the numerator of one fraction with the denominator of the other fraction, and vice versa: $2y = 18$ Divide each side by $2$ to solve for $y$: $y = 9$ Now, let's set up the proportion to find $z$: $\frac{z}{3.5} = \frac{3}{2}$ Get rid of the fractions by using the cross products property to multiply the numerator of one fraction with the denominator of the other fraction, and vice versa: $2z = 10.5$ Divide each side by $2$ to solve for $z$: $z = 5.25$