1. **State the problem:** We have parallelogram RSTU with sides labeled as follows: - Top side RS = $2a$ - Left side RU = $2b - 1$ - Bottom side ST = $3a - 5$ - Right side TU = $b + 3$ We need to find the values of $a$ and $b$. 2. **Recall properties of parallelograms:** Opposite sides are equal in length. 3. **Set up equations:** - Since RS and ST are opposite sides, $2a = 3a - 5$ - Since RU and TU are opposite sides, $2b - 1 = b + 3$ 4. **Solve for $a$:** $$2a = 3a - 5$$ Subtract $2a$ from both sides: $$\cancel{2a} = 3a - 5 - \cancel{2a}$$ $$0 = a - 5$$ Add 5 to both sides: $$a = 5$$ 5. **Solve for $b$:** $$2b - 1 = b + 3$$ Subtract $b$ from both sides: $$(2b - \cancel{1}) - b = \cancel{b} + 3 - b$$ $$b - 1 = 3$$ Add 1 to both sides: $$b = 4$$ 6. **Final answer:** $$a = 5, \quad b = 4$$