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Parallel Lines and Transversals

A free Geometry lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.

When a transversal crosses parallel lines, corresponding and alternate interior angles are congruent, while same-side interior angles are supplementary.

What you'll learn

Why it matters: Road markings, rail tracks, and tiled floors create parallel-line angle patterns that designers use to keep layouts aligned.

Worked example

Problem. Parallel lines are cut by a transversal. One same-side interior angle is 118 degrees. Find the other.

  1. Same-side interior angles are supplementary.
  2. They add to 180 degrees.
  3. 180 - 118 = 62.

Answer: 62 degrees

Practice problems

1. Corresponding angles formed by parallel lines are...

Choices: Congruent · Supplementary · Always 90 degrees · Unrelated

Show solution
  1. Warm-up: First identify exactly what the question is asking: Corresponding angles formed by parallel lines are...
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Corresponding angles have equal measures.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Congruent

2. If a corresponding angle is 73 degrees, what is its match?

Show solution
  1. Warm-up: First identify exactly what the question is asking: If a corresponding angle is 73 degrees, what is its match?
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Corresponding angles are congruent.
  4. Check the result by substituting or estimating: the response should match 73 and make sense in the original problem.

Answer: 73

3. Alternate interior angles are 5x and 110 degrees. Find x.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Alternate interior angles are 5x and 110 degrees. Find x.
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Set 5x = 110.
  4. Check the result by substituting or estimating: the response should match 22 and make sense in the original problem.

Answer: 22

4. Same-side interior angles include 125 degrees. What is the other angle?

Show solution
  1. Core Practice: First identify exactly what the question is asking: Same-side interior angles include 125 degrees. What is the other angle?
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. 180 - 125 = 55.
  4. Check the result by substituting or estimating: the response should match 55 and make sense in the original problem.

Answer: 55

5. Which angle pair is supplementary when lines are parallel?

Choices: Same-side interior · Alternate interior · Corresponding · Vertical

Show solution
  1. Challenge: First identify exactly what the question is asking: Which angle pair is supplementary when lines are parallel?
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Same-side interior angles add to 180 degrees.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Same-side interior

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