Chapter 6 Polygons and...
Transcript of Chapter 6 Polygons and...
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Chapter 6 – Polygons and Quadrilaterals.
6.1 – Properties of Polygons
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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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Classify polygons based on their sides and angles.
Find and use the measures of interior and exterior angles of polygons.
Objectives
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side of a polygon
vertex of a polygon
diagonal
regular polygon
concave
convex
Vocabulary
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A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints.
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side of the polygon - segments that forms a polygon
vertex of the polygon - common endpoint of two sides
Diagonal - A segment that connects any two nonconsecutive vertices
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You can name a polygon by the number of its sides.
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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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A polygon is concave if any part of a diagonal contains points in the exterior of the polygon.
(Concave – part of the shape is CAVED IN. )
If no diagonal contains points in the exterior, then the polygon is convex.
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A regular polygon is one that is both equilateral and equiangular. A regular polygon is always convex.
If a polygon is not regular, it is called irregular.
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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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Check It Out! Example 2b
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
irregular, concave
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