## Plane and Solid Figures

Plane geometry is the study of figures in the plane such as points, lines, line segments, rays, angles, triangles, quadrilaterals, and other polygons. To understand geometry, students need to understand its basic terms, which are used to define many other terms. A plane is a collection of points that forms a flat, continuous, and unending surface. A point is a location in space. A line is a straight, continuous, and unending collection of points.

A line segment is the part of a line between two points including the endpoints. A ray is part of a line that has one endpoint and continues in one direction without end. An angle is determined by two rays with a common endpoint called the vertex of the angle. However, each pair of rays with a common endpoint determines two angles, ∠n and ∠m as shown below.

The measure of an angle is determined by how much one ray of the angle must be rotated through the interior of the angle until it coincides with the other ray of the angle. An angle that forms a square corner is called a right angle. An angle that has a measure less than that of a right angle is called an acute angle. An angle that has a measure greater than that of a right angle is called an obtuse angle.

Polygons
At this grade level, a polygon is defined as a simple, closed figure formed by three or more line segments meeting only at their endpoints. The line segments are called sides of the polygon.

Polygons are named according to their number of sides: triangle, 3 sides; quadrilateral, 4 sides; pentagon, 5 sides; hexagon, 6 sides; heptagon, 7 sides; octagon, 8 sides. At this grade level, only triangles, quadrilaterals, pentagons, hexagons, and octagons are considered.

Quadrilaterals are classified according to the properties of their sides and angles. Parallel sides are described as sides that are always the same distance apart. Rectangles have four right angles and opposite sides parallel. Squares have 4 right angles, 4 congruent sides, and opposite sides parallel. Parallelograms have opposite sides parallel and opposite sides and opposite angles congruent.

At this grade level, triangles are classified only by the measures of their sides: equilateral—3 sides of the same length; isosceles—2 sides of the same length; scalene—no sides of the same length.

Solid Figures
At this grade level, only right solid figures are considered. This means that prisms have rectangular faces, that the curved surface of a cylinder is perpendicular to the bases, and that the line from the vertex of a pyramid or a cone lies over the center point of the base. The types of solid figures studied are rectangular prisms, square pyramids, cylinders, cones, and spheres. A cube is a special rectangular prism in which all faces are congruent. Prisms and pyramids are named according to the shapes of their bases.

Teaching Model 15.6: Solid Figures