Alternate Interior Angles and Parallel Lines

The page explores the relationship between parallel lines and the angles formed when they are cut by a transversal.

Definition: Alternate interior angles are pairs of angles formed when two lines are cut by a transversal.

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

Example: When parallel lines are cut by a transversal, corresponding angles measure 65 degrees.

Applications and Problem Solving

The final section focuses on practical applications and problem-solving using parallel lines and angle relationships.

Example: When EFG equals IHF at 35°, the lines EF and IH are parallel.

Highlight: The equality of corresponding angles is sufficient to prove that two lines are parallel.

Definition: Corresponding angles are pairs of angles in similar positions when two lines are cut by a transversal.

Adjacent Angles and Basic Relationships

This section introduces fundamental angle relationships and their properties in geometry. The content focuses on adjacent angles and their characteristics, complementary and supplementary angles.

Definition: Adjacent angles share a common vertex and side, lying on opposite sides of the shared ray.

Example: Angles XOY and YOZ are adjacent when they share vertex O and ray OY.

Vocabulary: Complementary angles are two angles whose measures sum to 90 degrees.

Highlight: Supplementary angles are two angles whose measures sum to 180 degrees.