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6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation
Lesson Quiz Holt Geometry
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Warm Up 1. A ? is a three-sided polygon.
2. A ? is a four-sided polygon. Evaluate each expression for n = 6. 3. (n – 4) 12 4. (n – 3) 90 Solve for a. 5. 12a + 4a + 9a = 100 triangle quadrilateral 24 270 4
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Objectives Classify polygons based on their sides and angles.
Find and use the measures of interior and exterior angles of polygons.
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Vocabulary side of a polygon vertex of a polygon diagonal
regular polygon concave convex
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Each segment that forms a polygon is a side of the polygon
Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.
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You can name a polygon by the number of its sides
You can name a polygon by the number of its sides. The table shows the names of some common polygons.
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A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints. Remember!
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Example 1A: Identifying Polygons
Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. polygon, hexagon
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Example 1B: Identifying Polygons
Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. polygon, heptagon
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Example 1C: Identifying Polygons
Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. not a polygon
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Check It Out! Example 1a Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides. not a polygon
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Check It Out! Example 1b Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides. polygon, nonagon
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Check It Out! Example 1c Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides. not a polygon
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All the sides are congruent in an equilateral polygon
All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular.
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A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex.
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Example 2A: Classifying Polygons
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, convex
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Example 2B: Classifying Polygons
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, concave
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Example 2C: Classifying Polygons
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. regular, convex
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Check It Out! Example 2a Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. regular, convex
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