1. **Problem Statement:** Given pairs of corresponding congruent angles and sides: $AZ = XY$, $WX = NO$, and variables $x, y, z$ representing side lengths. We need to: a) Find the scale factor. b) Find the values of $x, y, z$. c) Find the ratio of the perimeters. 2. **Understanding the problem:** We have two parallelograms and a triangle with given side lengths and variables. The sides $AZ$ and $XY$ are congruent, as are $WX$ and $NO$. The scale factor relates the corresponding sides of the shapes. 3. **Step a) Find the scale factor:** Assuming $WX = NO$ and given $WX = 10$ and $NO = 8$ (from the parallelograms), the scale factor $k$ from the larger to smaller shape is: $$k = \frac{NO}{WX} = \frac{8}{10} = \frac{4}{5}$$ 4. **Step b) Find values of $x, y, z$:** Since $AZ = XY$ and $AZ$ corresponds to $x$, $XY$ corresponds to $x$ as well. Using the scale factor $k = \frac{4}{5}$, the sides scale accordingly: - For side $x$: $$x = k \times 10 = \frac{4}{5} \times 10 = 8$$ - For side $y$: Given $y$ corresponds to side $6$ in the larger shape, scale down: $$y = k \times 6 = \frac{4}{5} \times 6 = \frac{24}{5} = 4.8$$ - For side $z$: Given $z$ corresponds to side $x$ in the larger shape (assumed 10), scale down: $$z = k \times 10 = 8$$ 5. **Step c) Find the ratio of the perimeters:** The ratio of perimeters is equal to the scale factor: $$\text{Ratio of perimeters} = k = \frac{4}{5}$$ **Final answers:** - Scale factor $k = \frac{4}{5}$ - $x = 8$ - $y = 4.8$ - $z = 8$ - Ratio of perimeters $= \frac{4}{5}$