Polygons
Study Guides
Big Picture Polygons consist of line segments connected only at their endpoints. Many types of polygons exist, with varying side and angle measurements. Using formulas, we can find the sum of the interior angles of a polygon.
Key Terms Polygon: Any closed planar figure made entirely of line segments that only intersect at the endpoints. Side: The line segment making up the polygon. Vertex (plural, vertices): The point where the segments intersect. Convex Polygon: A polygon where all the interior angles are less than 180°. Interior Angle: The angle inside of a closed figure with straight sides. Concave Polygon: A polygon where at least one interior angle is greater than 180°. Diagonal: A line segment that connects two nonconsecutive sides of a polygon. Exterior Angle: The angle formed by one side of a polygon and the extension of the adjacent side. Equilateral Polygon: All sides of the polygon are congruent. Equiangular Polygon: All interior angles of the polygon are congruent. Regular Polygon: A polygon that is equilateral and equiangular.
Polygons •
In a polygon, the sides can NEVER be curved. Line segments form the sides of the polygon.
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The polygon must also be closed.
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To name a polygon, the vertices are listed in consecutive order.
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A polygon lies within one plane.
Convex and Concave Polygons In a convex polygon, no section points inward.
A side connects consecutive vertices, while a diagonal connects nonconsecutive vertices. A concave polygon has a section that points inward toward the interior of the shape.
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Concave polygons have at least one diagonal outside the figure (the exterior line drawn in the figure below).
A concave polygon has a section that caves in.
This guide was created by Nicole Crawford, Jane Li, Amy Shen, and Zachary Wilson. To learn more about the student authors, visit http://www.ck12.org/ about/aboutus/team/interns.
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