## Plane Shapes

So far the study of number concepts has been the focus of second-grade mathematics. The study of geometry focuses on space and the figures and shapes that are a part of space. In the primary grades, geometric representations often take the form of drawings, which are very useful when modeling and solving a variety of real-world problems.

The point, the line, and the plane are the fundamental concepts of elementary geometry, sometimes called Euclidian geometry (after Euclid, who around 300 B.C.E. outlined the basic definitions and assumptions of geometry in his book, **Elements**).

A geometric point has no dimension; that is, it has no length, height, or width. A point cannot be measured or touched, it simply is a location in space. A line is made up of a straight path of an infinite number of points that extends in two directions with no endpoints. A line segment is part of a line contained between two points on the line. These points are the endpoints of the line segment. A line segment has length, but no width. A plane is a set of points that forms a flat surface infinitely wide and infinitely long. A plane has no boundary with respect to length and width, and it has no thickness.

Space is defined as the set of all points. Three-dimensional shapes that children study in elementary school are often called solid shapes, or figures. Children's study of geometry can be divided into two broad categories, plane geometry and solid geometry.

Plane geometry concerns itself with the study of two-dimensional shapes, or figures that lie in a plane. Common plane figures that children study in this grade include the rectangle, square, triangle, circle, and oval. Children learn that some plane shapes (polygons) have sides and vertices. Others, such as the circle, have no sides or vertices. (**Vertex** is the singular of **vertices**.) Two figures are said to be congruent if they can be superimposed so that they match exactly. This means that the two figures have exactly the same shape and the same size, differing only in position.

Plane figures can have line symmetry. A figure has line symmetry if there exists a line that the figure can be folded over so that one half of the figure matches the other half exactly. A square, for example, has more than one line of symmetry.

**Teaching Model 7.2:** Sides and Vertices