Adjacent sides are pairs of sides in a polygon or geometric shape that share a common vertex or endpoint. These sides are positioned next to each other and are connected by the common vertex. In a polygon, the sides that are not adjacent are called opposite sides.
In geometry, it is important to understand the properties of adjacent sides and how they relate to other parts of a shape. This understanding can help with solving problems involving polygons, such as finding the area, perimeter, or other measurements.
Definitions:
- Polygon: A closed, two-dimensional figure with straight sides and angles.
- Vertex: The point where two or more lines or sides intersect in a polygon.
- Adjacent sides: Pairs of sides in a polygon that share a common vertex and are positioned next to each other.
- Opposite sides: Sides in a polygon that are not adjacent to each other.
Examples:
- Triangle: In a triangle, there are three sides and three vertices. Each side is adjacent to the two other sides that share a common vertex with it. For example, in an equilateral triangle, all three sides are equal in length and are adjacent to each other.
- Quadrilateral: In a quadrilateral, there are four sides and four vertices. Each side is adjacent to the two other sides that share a common vertex with it. For example, in a rectangle, the opposite sides are parallel and equal in length, while the adjacent sides are perpendicular to each other and have different lengths.
- Pentagon: In a pentagon, there are five sides and five vertices. Each side is adjacent to the two other sides that share a common vertex with it. For example, in a regular pentagon, all five sides are equal in length and are adjacent to each other.
- Hexagon: In a hexagon, there are six sides and six vertices. Each side is adjacent to the two other sides that share a common vertex with it. For example, in a regular hexagon, all six sides are equal in length and are adjacent to each other.
- Octagon: In an octagon, there are eight sides and eight vertices. Each side is adjacent to the two other sides that share a common vertex with it. For example, in a regular octagon, all eight sides are equal in length and are adjacent to each other.
Quiz:
- Which of the following is not a polygon? a. Triangle b. Circle c. Quadrilateral d. Pentagon
- What is a vertex in a polygon? a. A point where two or more sides intersect b. A side that is not adjacent to any other sides c. A side that is parallel to another side d. The center of a polygon
- Which of the following statements is not true about adjacent sides in a polygon? a. They share a common vertex b. They are positioned next to each other c. They are opposite sides d. They have different lengths
- Which of the following shapes has three sides and three vertices? a. Triangle b. Quadrilateral c. Pentagon d. Hexagon
- In a rectangle, which of the following statements is not true? a. The opposite sides are parallel b. The opposite sides have different lengths c. The adjacent sides are perpendicular to each other d. The adjacent sides have the same length.
