1. **State the problem:** We have a large triangle with a base of 13 and two segments inside parallel to the base, creating smaller triangles with sides labeled 4, 6, 2, 6, 9, and unknowns $x$, $y$, and $z$. We need to solve for $x$, $y$, and $z$. 2. **Use the properties of similar triangles:** Since the segments are parallel to the base, the smaller triangles are similar to the large triangle and to each other. This means corresponding sides are proportional. 3. **Set up proportions:** - For the top small triangle with side $z$ and side 2, corresponding to the large triangle with side 4: $$\frac{z}{2} = \frac{4}{6}$$ - For the middle small triangle with side $x$ and side 6, corresponding to the large triangle with side 6: $$\frac{x}{6} = \frac{6}{9}$$ - For the right segment $y$ corresponding to side 9: $$\frac{y}{9} = \frac{6}{13}$$ 4. **Solve for $z$:** $$z = 2 \times \frac{4}{6} = 2 \times \frac{2}{3} = \frac{4}{3} \approx 1.3$$ 5. **Solve for $x$:** $$x = 6 \times \frac{6}{9} = 6 \times \frac{2}{3} = 4$$ 6. **Solve for $y$:** $$y = 9 \times \frac{6}{13} = \frac{54}{13} \approx 4.2$$ 7. **Final answers:** $$x = 4$$ $$y \approx 4.2$$ $$z \approx 1.3$$