Understanding Parallel Lines and Transversals

This comprehensive page explores the fundamental concepts of parallel lines and transversals, providing detailed explanations of various angle relationships. The content begins with the definition of parallel lines and progresses through different types of angles formed when intersected by a transversal.

Definition: Parallel lines are lines in the same plane that never intersect, indicated by arrow heads on both lines pointing in the same direction (symbolled as AB || CD).

Vocabulary: A transversal is a line that intersects two or more lines at different points.

Example: When parallel lines are cut by a transversal, corresponding angles are congruent (m∠1 = m∠2).

The page outlines several key theorems:

1. Corresponding angles are congruent when parallel lines are cut by a transversal.
2. Alternate interior angles are congruent (m∠4 = m∠5).
3. Alternate exterior angles are congruent (m∠2 = m∠7).
4. Consecutive interior angles are supplementary (m∠3 + m∠5 = 180°).
5. Consecutive exterior angles are supplementary (m∠2 + m∠8 = 180°).

Highlight: The page includes a practical example where m∠2 = 80°, demonstrating how to find all related angles using the principles of congruent and supplementary angles.

Example: When m∠2 = 80°, corresponding angles (m∠10, m∠12, m∠13, m∠15) are also 80°, while supplementary angles (m∠6, m∠8, m∠3, m∠14, m∠9, m∠11, m∠16) measure 100°.