**Table of Contents**Show

## Introduction to Linear Pairs

Linear pairs are a fundamental concept in geometry that are essential for understanding angles and their relationships. In geometry, angles are formed when two rays share a common endpoint. When two adjacent angles add up to form a straight line (180 degrees), they are known as linear pairs. Understanding linear pairs is crucial for solving geometric problems and proving theorems related to angles.

## Characteristics of Linear Pairs

Before delving into which pairs are considered linear, it is important to understand the characteristics of linear pairs:

**Adjacent Angles:**Linear pairs consist of two adjacent angles that share a common vertex and a common side.**Straight Angle:**The two angles in a linear pair must add up to 180 degrees, forming a straight angle.**Supplementary Angles:**Linear pairs are supplementary angles, meaning their measures add up to 180 degrees.

## Identifying Linear Pairs

To identify which pairs are considered linear, it is crucial to recognize the following criteria:

**Adjacent:**The angles must be adjacent, meaning they share a common side and vertex.**Straight Line:**The sum of the measures of the two angles must be 180 degrees, forming a straight line.**Supplementary:**The angles must be supplementary, adding up to 180 degrees.

## Examples of Linear Pairs

Here are some examples of pairs of angles that form linear pairs:

**Angle AOC and Angle COB:**In triangle ABC, if angle AOC measures 120 degrees, and angle COB measures 60 degrees, they form a linear pair as they add up to 180 degrees.**Angle PQR and Angle RQS:**In quadrilateral PQRS, if angle PQR measures 90 degrees, and angle RQS measures 90 degrees, they form a linear pair as they add up to 180 degrees.**Angle XYZ and Angle ZYW:**In triangle XYZ, if angle XYZ measures 30 degrees, and angle ZYW measures 150 degrees, they form a linear pair as they add up to 180 degrees.

## Non-Examples of Linear Pairs

Not all pairs of adjacent angles form linear pairs. Here are some examples of non-linear pairs:

**Angle ABC and Angle CDE:**In triangle ABC, if angle ABC measures 45 degrees, and angle CDE measures 135 degrees, they do not form a linear pair as they do not add up to 180 degrees.**Angle DEF and Angle FGH:**In quadrilateral DEFG, if angle DEF measures 60 degrees, and angle FGH measures 120 degrees, they do not form a linear pair as they do not add up to 180 degrees.**Angle LMN and Angle NOP:**In triangle LMN, if angle LMN measures 70 degrees, and angle NOP measures 110 degrees, they do not form a linear pair as they do not add up to 180 degrees.

## Summary

In conclusion, understanding linear pairs is essential in geometry to identify relationships between angles and solve geometric problems efficiently. Linear pairs consist of two adjacent angles that form a straight line and add up to 180 degrees. By recognizing the criteria for linear pairs and practicing identifying examples, you can enhance your geometric skills and tackle angle-related problems with ease.