In geometry, a base is a side of a polygon or a face of a polyhedron that is used as a reference or starting point for other measurements or constructions. It is often the bottom or lowermost side of a shape, but it does not have to be. The base of a triangle, for example, can be any of its three sides, and the base of a pyramid can be any of its four faces.
Here are some definitions of key terms related to bases in geometry:
- Polygon: a two-dimensional shape with straight sides and angles. A polygon is named according to the number of sides it has. For example, a triangle has three sides, a quadrilateral has four sides, and a hexagon has six sides.
- Polyhedron: a three-dimensional shape with flat faces and straight edges. A polyhedron is named according to the number of faces it has. For example, a tetrahedron has four faces, a cube has six faces, and an octahedron has eight faces.
- Vertex: the point where two or more sides of a polygon or edges of a polyhedron meet.
- Edge: the line segment formed by the intersection of two faces of a polyhedron.
- Face: a flat surface of a polyhedron.
Here are five examples of base in geometry:
- Triangle: A triangle is a polygon with three sides and three vertices. The base of a triangle can be any of its three sides, and the other two sides are called the legs. For example, in the triangle shown below, side BC is the base and sides AB and AC are the legs.
/
/
/____
A C | | | B
- Pyramid: A pyramid is a polyhedron with a polygonal base and triangular faces. The base of a pyramid can be any of its faces, and the other faces are called the lateral faces. For example, in the pyramid shown below, quadrilateral ABCD is the base and triangles AEB, AFC, AGD, and BHC are the lateral faces./
/B
/
/\ /
/E \ /F
//____
A C G |
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H D - Prism: A prism is a polyhedron with two congruent, parallel, and polygonal bases connected by lateral faces that are parallelograms. The bases of a prism are the top and bottom faces, and the lateral faces are the sides. For example, in the prism shown below, quadrilateral ABCD is the top base, quadrilateral EFGH is the bottom base, and rectangles ADEF, BEGF, and CHDG are the lateral faces.
