1. **State the problem:** We have two similar quadrilaterals with corresponding sides proportional. We need to find the lengths of $x$, $y$, and $z$ in the smaller quadrilateral given the larger quadrilateral's sides. 2. **Identify corresponding sides:** - $x$ corresponds to 49 - $y$ corresponds to 56 - $z$ corresponds to 28 - The known side in the smaller quadrilateral is 21, corresponding to 49 in the larger one. 3. **Find the scale factor:** The scale factor from the larger to the smaller quadrilateral is $$\frac{21}{49} = \frac{3}{7}.$$ This means each side length in the smaller quadrilateral is $\frac{3}{7}$ of the corresponding side in the larger quadrilateral. 4. **Calculate $x$:** $$x = 49 \times \frac{3}{7} = \cancel{49}^7 \times 3 = 7 \times 3 = 21.$$ 5. **Calculate $y$:** $$y = 56 \times \frac{3}{7} = \cancel{56}^7 \times 3 = 8 \times 3 = 24.$$ 6. **Calculate $z$:** $$z = 28 \times \frac{3}{7} = \cancel{28}^7 \times 3 = 4 \times 3 = 12.$$ **Final answers:** - $x = 21$ - $y = 24$ - $z = 12$