Basic Geometry: Introduction to Basic Geometry Concepts

Introductory Geometry for Elementary Schoolers

Patterns and Reasoning

From the beginning, students learn to compare and contrast shapes and their attributes, and to draw conclusions from their analysis. Kindergarteners compare triangles of different sizes or colors and conclude that size and colors aren't attributes of triangles, but having three sides and three angles are. A few years later, these students may compare rectangles and rhombuses, and realize that more than one classification of polygons can have four sides and four angles.

Here are some shapes introduced in basic elementary geometry. They're grouped logically, not necessarily in the order in which they're learned.

Plane Geometry

Elementary schoolers may not learn the phrase 'plane geometry,' but they're introduced to its basic elements and concepts. These shapes are 2-dimensional and can lie on a flat surface (a 'plane').

Lines

Students draw straight lines with rulers; however, in geometry, they learn that they can't truly draw a line because it extends into infinity on either end. They actually draw line segments. Other concepts relating to lines are points, endpoints and rays. Lines may intersect or they may be parallel. Some lines that intersect are perpendicular to one another.

Angles

An angle is comprised of two rays that have one common endpoint. Although elementary schoolers may be introduced to straight angles, more common are right, acute and obtuse angles.

Polygons

Polygons are closed shapes that have three or more sides. The primary polygons that K-6 students learn about are triangles and quadrilaterals - shapes with three or four sides. Quadrilaterals include squares, rectangles, parallelograms, rhombi and trapezoids. After learning these basic geometric shapes, students learn how to find perimeter and area. Often pentagons, hexagons, octagons and other '-agons' are presented and decomposed to triangles and quadrilaterals.

Circles

A circle is a closed curved line. Every point on that line is the same distance from the center of the circle. Elementary schoolers learn basic information about circles, including radius, diameter and circumference.

Solid Geometry

As with plane geometry, elementary schoolers may not be introduced to the phrase 'solid geometry.' However, they learn to identify 3-dimensional figures as 'solids' as early as kindergarten.

Polyhedrons

Polyhedrons are to solid geometry as polygons are to plane geometry. Polyhedrons can be defined as 3-dimensional figures that have three or more flat sides. In actuality, they have at least four flat sides, each of which is a polygon. Polyhedrons introduced in elementary grades include cubes, prisms and pyramids. Students learn to measure the surface area and volume of these figures.

Curved Figures

Curved solid figures introduced as early as kindergarten include spheres, cylinders and cones. Unlike plane figures and polyhedrons, finding volume and surface area of curved solids is generally not taught until eighth grade.