Adjacent Sides — Definition, Formula & Examples
Adjacent sides are two sides of a polygon that meet at the same vertex (corner point). For example, in a rectangle, the length and the width that share a corner are adjacent sides.
In a polygon, two sides are adjacent if and only if they share exactly one common endpoint (vertex). Every side of an -sided polygon has exactly two adjacent sides.
Example
Problem: A quadrilateral ABCD has vertices A, B, C, and D in order. Identify all pairs of adjacent sides.
Step 1: List the sides of quadrilateral ABCD.
Step 2: At each vertex, find the two sides that meet. At vertex A, sides AB and DA meet. At vertex B, sides AB and BC meet. At vertex C, sides BC and CD meet. At vertex D, sides CD and DA meet.
Step 3: List the adjacent pairs. Notice that sides like AB and CD do NOT share a vertex — those are called opposite sides, not adjacent sides.
Answer: The four pairs of adjacent sides are: AB & BC, BC & CD, CD & DA, and DA & AB.
Why It Matters
Knowing which sides are adjacent is essential when applying properties of specific quadrilaterals. For instance, a kite is defined as having two distinct pairs of consecutive (adjacent) sides that are equal in length. In parallelograms, adjacent sides determine both the perimeter formula and the relationship between consecutive angles.
Common Mistakes
Mistake: Confusing adjacent sides with opposite sides in quadrilaterals.
Correction: Adjacent sides share a vertex. Opposite sides do not touch at all. In rectangle ABCD, sides AB and CD are opposite, while AB and BC are adjacent.