Geometry: Vertical Angles and Linear Pairs

Study Notes

Angle Relationships

Vertical Angles: Formed by two intersecting lines. Non-adjacent angles with opposite rays.
Linear Pairs: Two adjacent angles whose non-common sides form a straight angle.

Theorems

If two angles are congruent, they share the same measure.
Vertical angles are always congruent.
Angles in a linear pair have a sum of 180°.

Angle Classifications

Acute Angle: Less than 90°.
Right Angle: Exactly 90°.
Obtuse Angle: Greater than 90° but less than 180°.
Straight Angle: Exactly 180°.

Adjacent Angles

Two angles are adjacent if they share a common ray and vertex.

Complementary and Supplementary Angles

Complementary Angles: Two angles that sum to 90°. Not required to be adjacent.
Supplementary Angles: Two angles that sum to 180°.

Angle Relationships in Diagrams

Use diagrams to identify and solve for missing angle measures and variables.
Complement of an angle: The degree measure that, when added to the angle, equals 90°.

Problem Solving Tips

For complementary angles, if one angle measure is known, subtract from 90° to find the other.
For supplementary angles, if one angle measure is known, subtract from 180° to find the other.

Exploration Resources

Interactive links provided for exploring vertical angles and linear pairs.
Visual aids can enhance understanding of complementary angles and their relationships.

Description

This quiz tests your understanding of vertical angles and linear pairs. You'll need to identify the definitions and properties of these types of angles in geometry. Perfect for students looking to reinforce their knowledge on angle relationships.