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Grade 10 · lesson 1 of 4

Use Parallelism to Match Corresponding Angles

A transversal crossing parallel lines creates equal corresponding angles.

About 20 minutes, plus any extended practice

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Supplied materials

  • Paper or a browser scratch area; a calculator is optional unless rounding is requested.
  • Supplied teaching case: Two parallel lines are cut by a transversal. One angle is 35°. Find its corresponding angle. Candidate answers: (A) 145 ° (B) 35 ° (C) 45 ° (D) 55 °.
  • Independent check inputs: Two parallel lines are cut by a transversal. One angle is 37°. Find its corresponding angle. Candidate answers: (A) 143 ° (B) 37 ° (C) 47 ° (D) 53 °.

Learn the idea

Parallel-line and triangle theorems connect geometric conditions to numerical equations. Some side and angle values are impossible, so reasoning must check the defining configuration rather than rely only on arithmetic. A transversal crossing parallel lines creates equal corresponding angles. The parallel condition is what licenses this equality; a similar-looking nonparallel drawing does not supply it.

Here is the method on the supplied teaching case. Corresponding angles are equal when the lines are parallel. Therefore the corresponding angle is 35°. Without parallelism, this inference would not be warranted.

Locate corresponding positions at the two crossings before equating angles. An angle’s adjacent supplement is different; mark the parallel lines so the reason is part of the argument.

  1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
  2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
  3. Solve the independent check with its changed inputs before revealing feedback.
  4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
Worked example

See the method in action

Teaching case: Two parallel lines are cut by a transversal. One angle is 35°. Find its corresponding angle. Candidate answers: (A) 145 ° (B) 35 ° (C) 45 ° (D) 55 °. Solution: Corresponding angles are equal when the lines are parallel. Therefore the corresponding angle is 35°. Without parallelism, this inference would not be warranted. The final answer is 35 °. Locate corresponding positions at the two crossings before equating angles. An angle’s adjacent supplement is different; mark the parallel lines so the reason is part of the argument.

Your turn

Check your reasoning

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Helpful tips
  • A transversal crossing parallel lines creates equal corresponding angles.
  • Locate corresponding positions at the two crossings before equating angles.
Two parallel lines are cut by a transversal. One angle is 37°. Find its corresponding angle.

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

37 °

Corresponding angles are equal when the lines are parallel. Therefore the corresponding angle is 37°. Without parallelism, this inference would not be warranted.

Take it further

Changed-input task: Two parallel lines are cut by a transversal. One angle is 49°. Find its corresponding angle. Candidate answers: (A) 131 ° (B) 41 ° (C) 49 ° (D) 59 °. Show the mathematical reason, not only the selected answer. Expected result: 49 °. Corresponding angles are equal when the lines are parallel. Therefore the corresponding angle is 49°. Without parallelism, this inference would not be warranted.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.

More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. Two parallel lines are cut by a transversal. One angle is 39°. Find its corresponding angle.
Need a hint?
  • A transversal crossing parallel lines creates equal corresponding angles.
  • Locate corresponding positions at the two crossings before equating angles.
2. Two parallel lines are cut by a transversal. One angle is 41°. Find its corresponding angle.
Need a hint?
  • A transversal crossing parallel lines creates equal corresponding angles.
  • Locate corresponding positions at the two crossings before equating angles.
3. Two parallel lines are cut by a transversal. One angle is 43°. Find its corresponding angle.
Need a hint?
  • A transversal crossing parallel lines creates equal corresponding angles.
  • Locate corresponding positions at the two crossings before equating angles.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

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