This worksheet is designed to practice the Triangle Proportionality Theorem, which states that if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.
I will solve for `x` in each of the 8 problems by setting up and solving proportions based on this theorem.
---
Problem 1
The line segment of length `x` is parallel to the side of length 12. It divides the other two sides into segments of lengths 6 and 8.
- The proportion is: `x / 12 = 6 / (6 + 8)`
- Simplify: `x / 12 = 6 / 14`
- Solve for `x`: `x = 12 * (6 / 14) = 72 / 14 = 36 / 7 ≈ 5.14`
---
Problem 2
The line segment of length 5 is parallel to the side of length `x`. It divides the other two sides into segments of lengths 3 and 15.
- The proportion is: `5 / x = 3 / (3 + 15)`
- Simplify: `5 / x = 3 / 18 = 1 / 6`
- Solve for `x`: `x = 5 * 6 = 30`
---
Problem 3
The line segment of length `x` is parallel to the side of length 20. It divides the other two sides into segments of lengths 8 and 35.
- The proportion is: `x / 20 = 8 / (8 + 35)`
- Simplify: `x / 20 = 8 / 43`
- Solve for `x`: `x = 20 * (8 / 43) = 160 / 43 ≈ 3.72`
---
Problem 4
The line segment of length `x` is parallel to the side of length 9. It divides the other two sides into segments of lengths 3 and 5.
- The proportion is: `x / 9 = 3 / (3 + 5)`
- Simplify: `x / 9 = 3 / 8`
- Solve for `x`: `x = 9 * (3 / 8) = 27 / 8 = 3.375`
---
Problem 5
The line segment of length 20 is parallel to the side of length `x`. It divides the other two sides into segments of lengths 15 and 30.
- The proportion is: `20 / x = 15 / (15 + 30)`
- Simplify: `20 / x = 15 / 45 = 1 / 3`
- Solve for `x`: `x = 20 * 3 = 60`
---
Problem 6
The line segment of length 2 is parallel to the side of length `x`. It divides the other two sides into segments of lengths 6 and 8.
- The proportion is: `2 / x = 6 / (6 + 8)`
- Simplify: `2 / x = 6 / 14 = 3 / 7`
- Solve for `x`: `x = 2 * (7 / 3) = 14 / 3 ≈ 4.67`
---
Problem 7
The line segment of length `x` is parallel to the side of length 10. It divides the other two sides into segments of lengths 15 and 4.
- The proportion is: `x / 10 = 15 / (15 + 4)`
- Simplify: `x / 10 = 15 / 19`
- Solve for `x`: `x = 10 * (15 / 19) = 150 / 19 ≈ 7.89`
---
Problem 8
The line segment of length 3 is parallel to the side of length `x`. It divides the other two sides into segments of lengths 4 and 5.
- The proportion is: `3 / x = 4 / (4 + 5)`
- Simplify: `3 / x = 4 / 9`
- Solve for `x`: `x = 3 * (9 / 4) = 27 / 4 = 6.75`
---
Final Answers:
1. $ x = \frac{36}{7} \approx 5.14 $
2. $ x = 30 $
3. $ x = \frac{160}{43} \approx 3.72 $
4. $ x = \frac{27}{8} = 3.375 $
5. $ x = 60 $
6. $ x = \frac{14}{3} \approx 4.67 $
7. $ x = \frac{150}{19} \approx 7.89 $
8. $ x = \frac{27}{4} = 6.75 $
Parent Tip: Review the logic above to help your child master the concept of triangle proportionality theorem worksheet answers.
