1. **State the problem:** We have two similar parallelograms $WXYZ \sim MNOP$. We need to list pairs of corresponding congruent angles, write ratios of corresponding sides, find the scale factor, find values of $x$, $y$, and $z$, and find the ratio of the perimeters. 2. **List pairs of corresponding congruent angles:** Since $WXYZ \sim MNOP$, corresponding angles are congruent: $$\angle W \cong \angle M$$ $$\angle X \cong \angle N$$ $$\angle Y \cong \angle O$$ $$\angle Z \cong \angle P$$ 3. **Write ratios of corresponding sides:** Given the sides correspond as $WX = NO = YZ = MP$, the ratios of corresponding sides are equal: $$\frac{WX}{NO} = \frac{YZ}{MP}$$ 4. **Find the scale factor:** From the problem, the scale factor is given as $\frac{4}{5}$. 5. **Find values of $x$, $y$, and $z$:** Using the scale factor $\frac{4}{5}$ and the given values: - For $x$: Since $x$ corresponds to a side of length 10 in $MNOP$ (assuming from scale), we have $$x = \frac{4}{5} \times 10 = 8$$ - For $y$: Given $y = 4.8$ (already provided), consistent with scale factor. - For $z$: Given $z = 8$ (already provided), consistent with scale factor. 6. **Find the ratio of the perimeters:** The ratio of perimeters of similar figures equals the scale factor: $$\text{Ratio of perimeters} = \frac{4}{5}$$ **Final answers:** - Corresponding angles: $\angle W \cong \angle M$, $\angle X \cong \angle N$, $\angle Y \cong \angle O$, $\angle Z \cong \angle P$ - Ratios of corresponding sides: $\frac{WX}{NO} = \frac{YZ}{MP} = \frac{4}{5}$ - Scale factor: $\frac{4}{5}$ - Values: $x=8$, $y=4.8$, $z=8$ - Ratio of perimeters: $\frac{4}{5}$