What is the meaning of linear pair?
A linear pair is a geometric concept involving two adjacent angles that form a straight line. Here's the detailed explanation:
Definition: A linear pair consists of two adjacent angles whose non-common sides are opposite rays.
Key characteristics: 1. The angles must be adjacent (share a common vertex and side) 2. Their non-common sides form a straight line (180°) 3. The angles are supplementary - they add up to 180°
Visual example: Imagine a straight line with another line coming out from a point on it: - The straight line creates two angles on either side - These two angles form a linear pair - Together they make a straight angle (180°)
Mathematical representation: If angle A and angle B form a linear pair, then: ∠A + ∠B = 180°
Properties: - Linear pairs are always supplementary - The angles share a common vertex and arm - They always form a straight line
Real-world examples: - The hands of a clock at 6:00 - they form a straight line - A book opened flat - the two pages form a linear pair - Scissors when fully opened - the two blades form a linear pair
Important note: All linear pairs are supplementary, but not all supplementary angles form a linear pair. Supplementary angles just need to add to 180° - they don't have to be adjacent.
Understanding linear pairs is fundamental in geometry for solving angle problems and proving various geometric theorems!