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Corresponding Angles

Master corresponding angles with interactive lessons and practice problems! Angles 1–8 are labeled on two parallel horizontal lines intersected by a transversal as follows: at the upper intersection, ∠1 is top-left, ∠2 top-right, ∠3 bottom-right, ∠4 bottom-left; at the lower intersection, ∠5 top-left, ∠6 top-right, ∠7 bottom-right, ∠8 bottom-left.

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Corresponding Angles

Study Guide

Key Definition

Corresponding angles are formed when two parallel lines are intersected by a third line called the transversal. They occupy the same relative position. When two parallel lines are intersected by a transversal, the resulting corresponding angles are congruent.

Important Notes

Corresponding angles are equal when the lines are parallel.
For each pair of corresponding angles, one angle is an exterior angle and the other is an interior angle.

Mathematical Notation

$\angle$ denotes an angle.

$\cong$ denotes congruence.

Why It Works

The Corresponding Angles Postulate states that if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. This is because each angle occupies the same relative position at each intersection.

Remember

If two parallel lines are cut by a transversal, the corresponding angles are equal.

Quick Reference

Converse of Corresponding Angles Postulate:$\angle1 \cong \angle5$ implies the lines are parallel

Understanding Corresponding Angles

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Video explanation of this concept

Beginner

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Beginner Explanation

Corresponding angles are angles that are in the same relative position at an intersection of a transversal. In our diagram: upper intersection has ∠1 (top-left), ∠2 (top-right), ∠3 (bottom-right), ∠4 (bottom-left); lower intersection has ∠5 (top-left), ∠6 (top-right), ∠7 (bottom-right), ∠8 (bottom-left).

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following pairs of angles are corresponding angles?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $\angle1 \cong \angle5$ and $\angle3 \cong \angle7$, are the lines parallel?

Challenge Quiz

Single Choice Quiz

Advanced

If $\angle2 \cong \angle6$, $\angle3 \cong \angle7$, and $\angle4 \cong \angle8$, are the lines parallel?

Recap

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