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A part of springboard® course 1 math skills workshop unit 5, focusing on two-dimensional figures and polygons. It covers the basics of planes, two-dimensional figures, and polygons, including their definitions, properties, and classifications. The document also includes examples and practice exercises to help students understand the concepts.
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A plane is a flat surface that extends infinitely in all directions. A parallelogram like the one below is often used to model a plane, but remember that a plane—unlike a parallelogram—has no boundaries or sides. A plane figure or two-dimensional figure is a figure that lies completely in one plane. When you draw, either by hand or with a computer program, you draw two-dimensional figures. Blueprints are two-dimensional models of real-life objects. Polygons are closed, two-dimensional figures formed by three or more line segments that intersect only at their endpoints. These figures are polygons. These figures are not polygons. This is not a polygon because it is an open figure. A heart is not a polygon because it is has curves. A circle is not a polygon because it is made of a curve. Polygons are named by the number of sides and angles they have. A polygon always has the same number of sides as angles. Listed on the next page are the most common polygons. Each of the polygons shown is a regular polygon. All the angles of a regular polygon have the same measure and all the sides are the same length.
Two-Dimensional Figures (continued) Triangle 3 sides; 3 angles Quadrilateral 4 sides; 4 angles Pentagon 5 sides; 5 angles Hexagon 6 sides; 6 angles Heptagon 7 sides; 7 angles Octagon 8 sides; 8 angles Nonagon 9 sides; 9 angles Decagon 10 sides; 10 angles Classify the polygon. Step 1: Count the number of sides. Step 2: Identify a polygon with 6 sides. Solution: The polygon is a hexagon. The polygon has 6 sides. A hexagon has 6 sides.
Quadrilaterals are classified by the number of pairs of parallel sides that they have. Parallel sides never meet and remain the same distance apart. Parallelogram (2 pairs of parallel sides) Trapezoid (1 pair of parallel sides) Neither a parallelogram nor a trapezoid (0 pairs of parallel sides) Parallelograms can further be classified by the number of equal sides and by the number of right angles that they have. Rhombus (4 equal sides) Rectangle (4 right angles) Square (4 equal sides and 4 right angles)