Learn on PengiBig Ideas Math, Advanced 2Chapter 3: Angles and Triangles

Section 3.1: Parallel Lines and Transversals

In this Grade 7 lesson from Big Ideas Math, Advanced 2, students learn how to identify and find the measures of angles formed when parallel lines are cut by a transversal, including corresponding angles, interior angles, and exterior angles. Students apply the properties of corresponding angles, supplementary angles, and vertical angles to calculate unknown angle measures in multi-step problems. The lesson builds foundational geometry vocabulary and reasoning skills within Chapter 3: Angles and Triangles.

Section 1

Definition: Transversals

Property

A transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects two lines, it creates eight angles at the two intersection points.

Examples

Section 2

Parallel Lines

Property

Parallel Lines are lines in the same plane that never intersect, no matter how far they are extended. Parallel lines are always the same distance apart and run in the same direction. We use the symbol \parallel to indicate that two lines are parallel. If line aa is parallel to line bb, we write aba \parallel b.

Examples

Section 3

Vertical Angles

Property

Vertical angles are opposite angles formed when two lines intersect. Vertical angles are always congruent: 1=3\angle 1 = \angle 3 and 2=4\angle 2 = \angle 4.

Examples

Book overview

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Chapter 3: Angles and Triangles

  1. Lesson 1Current

    Section 3.1: Parallel Lines and Transversals

  2. Lesson 2

    Section 3.2: Angles of Triangles

  3. Lesson 3

    Section 3.3: Angles of Polygons

  4. Lesson 4

    Section 3.4: Using Similar Triangles

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Definition: Transversals

Property

A transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects two lines, it creates eight angles at the two intersection points.

Examples

Section 2

Parallel Lines

Property

Parallel Lines are lines in the same plane that never intersect, no matter how far they are extended. Parallel lines are always the same distance apart and run in the same direction. We use the symbol \parallel to indicate that two lines are parallel. If line aa is parallel to line bb, we write aba \parallel b.

Examples

Section 3

Vertical Angles

Property

Vertical angles are opposite angles formed when two lines intersect. Vertical angles are always congruent: 1=3\angle 1 = \angle 3 and 2=4\angle 2 = \angle 4.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 3: Angles and Triangles

  1. Lesson 1Current

    Section 3.1: Parallel Lines and Transversals

  2. Lesson 2

    Section 3.2: Angles of Triangles

  3. Lesson 3

    Section 3.3: Angles of Polygons

  4. Lesson 4

    Section 3.4: Using Similar Triangles