Understanding Linear Pairs: Definition, Properties, and Applications in Math and Beyond

Linear Pair

Two adjacent angles that form a straight line and add to 180

A linear pair refers to a pair of adjacent angles whose non-common sides form a straight line. In simple terms, it means two angles are said to be a linear pair if they add up to 180 degrees and share a common vertex and one common side.

For example, let’s consider a line AB, and two adjacent angles on the line, angle ABD and angle DBC. If these angles share the common vertex D and one common side BD, then they can be considered as a linear pair because they form a straight line, and their sum is equal to 180 degrees.

The concept of a linear pair is applicable in various fields, including geometry, physics, mathematics, and engineering. It is essential to understand linear pairs to solve problems that involve angles, lines, and parallel lines.

Some properties associated with linear pairs include:

1. The angles in a linear pair are supplementary, meaning that their sum is 180 degrees.
2. The two angles in a linear pair can also be called adjacent angles.
3. If two angles are adjacent and form a linear pair, then they are always supplementary.
4. The non-common arms of adjacent angles in a linear pair form opposite rays.

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