A linear pair of angles follows specific rules, based on their formation and relationship:
Defining Linear Pairs
- Linear pairs are formed when two lines intersect at a single point.
- The angles in a linear pair are adjacent (next to each other) after the intersection.
- These angles share a common vertex and a common side.
The Key Rule
- The sum of the angles in a linear pair always equals 180°. This is the fundamental rule that defines their relationship.
Example
Imagine two lines crossing each other. The two adjacent angles created on one side of the line together form a linear pair. If one of these angles measures 60°, then the other must measure 120° because 60° + 120° = 180°.
Rules Summarized
| Rule | Description |
|---|---|
| Formation | Two lines intersect at a point. |
| Adjacency | The angles are next to each other, sharing a common side and vertex. |
| Sum of Angles | The angles of a linear pair add up to 180°. |
Understanding these rules is essential for solving various geometry problems, particularly those involving lines, angles, and triangles. The concept of linear pairs is a cornerstone in geometric proofs and calculations.
