Application
Using Angle Relationships to Prove Lines Are Parallel

Using Angle Relationships to Prove Lines Are Parallel Problem Set


student working on math

For problems 1–3:

  1. Write an equation to solve for x.
  2. Choose a sentence from the list below to justify your equation.
  3. Find the indicated values.

Possible justifications:
  1. If alternate interior angles are congruent, then a transversal intersected parallel lines.
  2. If alternate exterior angles are congruent, then a transversal intersected parallel lines.
  3. If corresponding angles are congruent, then a transversal intersected parallel lines.
  4. If same-side interior angles are supplementary, then a transversal intersected parallel lines.

Example: Find x so that c ∥ d.

example

  1. Equation to solve for x: 8x + 80 + 12x − 40 = 180
  2. Justification #4: If same-side interior angles are supplementary, then a transversal intersected parallel lines.
  3. x = 7

    8x + 80 + 12x − 40   =  180
    20x + 4   =  180
    20x   =  180
    x   =  180

 

1. Find x so that w ∥ a.

figure 1

  1. Equation to solve for x: ________________
  2. Justification ___ : ________________
  3. x = ___

2. Find x so that t ∥ p.

figure 2

  1. Equation to solve for x: ________________
  2. Justification ___ : ________________
  3. x = ___

3. Given: m∠1 = (15x − 7)° and m∠2 = (8x + 21)°
Find x so that l ∥ m. Then, find m∠2.

figure 3

  1. Equation to solve for x: ________________
  2. Justification ___ : ________________
  3. x = ___
    m∠2 = ___

 

For problems 4–6: Determine which lines or segments are parallel. Explain your reasoning.

4. Which lines are parallel? Explain your reasoning.

figure 4

5. Which lines are parallel? Explain your reasoning.

figure 5

6. Which lines (or segments) are parallel? Explain your reasoning.

figure 6

 

For problems 7–8: Provide the appropriate reasons to complete the two-column proof.

7. Given: ∠2 and ∠4 are supplementary
Prove: t ∥ l figure 7

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 figure 8

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 figure 9

This activity is also available in a printable document.

 

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