Using Angle Relationships to Prove Lines Are Parallel Problem Set

For problems 1–3:
- Write an equation to solve for x.
- Choose a sentence from the list below to justify your equation.
- Find the indicated values.
Using Angle Relationships to Prove Lines Are Parallel Problem Set
For problems 1–3:
Example: Find x so that c ∥ d.
8x + 80 + 12x − 40 | = | 180 |
20x + 4 | = | 180 |
20x | = | 180 |
x | = | 180 |
1. Find x so that w ∥ a.
2. Find x so that t ∥ p.
3. Given: m∠1 = (15x − 7)° and m∠2 = (8x + 21)°
Find x so that l ∥ m. Then, find m∠2.
For problems 4–6: Determine which lines or segments are parallel. Explain your reasoning.
4. Which lines are parallel? Explain your reasoning.
5. Which lines are parallel? Explain your reasoning.
6. Which lines (or segments) are parallel? Explain your reasoning.
For problems 7–8: Provide the appropriate reasons to complete the two-column proof.
7. Given: ∠2 and ∠4 are supplementary
Prove: t ∥ l
Statements | Reasons |
1. ∠2 and ∠4 are supplementary | 1. |
2. ∠5 and ∠4 form a linear pair. | 2. |
3. ∠5 and ∠4 are supplementary. | 3. |
4. ∠2 ≅ ∠5 | 4. |
5. t ∥ l | 5. |
8. Given: x ∥ y; ∠1 ≅ ∠2
Prove: g ∥ h
Statements | Reasons |
1. x ∥ y; ∠1 ≅ ∠2 | 1. |
2. ∠2 ≅ ∠3 | 2. |
3. ∠1 ≅ ∠3 | 3. |
4. g ∥ h | 4. |
For problem 9: Use the given information to write a paragraph to prove w ∥ x.
9. Given: ∠1 and ∠2 are supplementary
Prove: w ∥ x
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