Angle Relationships in Parallel Lines - Geometry | Luna Learn 24

Angle Relationships in Parallel Lines

In this lesson, we will explore Angle Relationships in Parallel Lines. We will cover the concepts of Alternate Interior Angles, Alternate Exterior Angles, and Corresponding Angles. These relationships are fundamental in geometry and help in understanding various geometric proofs and properties.

Outline

Definition of Alternate Interior Angles
Definition of Alternate Exterior Angles
Definition of Corresponding Angles
Examples and Diagrams
Exercises with Solutions
Homework and Revision Section

1. Alternate Interior Angles

Alternate interior angles are angles that lie on opposite sides of the transversal and inside the parallel lines. These angles are always equal.

Example 1: Identifying Alternate Interior Angles

In the diagram below, identify the alternate interior angles if one angle measures \( 70^\circ \).

Alternate interior angles are equal. Thus, the measure of the other alternate interior angle is \( 70^\circ \).

2. Alternate Exterior Angles

Alternate exterior angles are angles that lie on opposite sides of the transversal and outside the parallel lines. These angles are also always equal.

Example 2: Identifying Alternate Exterior Angles

In the diagram, find the measure of the alternate exterior angle if one of them measures \( 120^\circ \).

Alternate exterior angles are equal. Thus, the measure of the other alternate exterior angle is \( 120^\circ \).

3. Corresponding Angles

Corresponding angles are angles that lie on the same side of the transversal and in corresponding positions relative to the parallel lines. These angles are equal.

Example 3: Identifying Corresponding Angles

Determine the measure of corresponding angles if one angle measures \( 80^\circ \).

Corresponding angles are equal. Therefore, the measure of the other corresponding angle is \( 80^\circ \).

Exercises

Exercise 1: Given two parallel lines cut by a transversal, if one alternate interior angle measures \( 85^\circ \), find the measure of the other alternate interior angle.

Alternate interior angles are equal. Therefore, the measure of the other angle is \( 85^\circ \).

Exercise 2: Find the measure of the alternate exterior angle if one of the angles measures \( 110^\circ \).

Alternate exterior angles are equal. Thus, the other angle measures \( 110^\circ \).

Exercise 3: Determine the measure of corresponding angles if one angle is \( 60^\circ \).

Corresponding angles are equal. Therefore, the other angle measures \( 60^\circ \).