Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Section 3-1 Symmetry 3.1 Symmetry in Polygons.

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Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Section 3-1 Symmetry 3.1 Symmetry in Polygons

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Definitions Def: A polygon is a plane figure formed from three or more segments such that each segment intersects exactly two other segments, one at each endpoint, and no two segments with a common endpoint are collinear. 3.1 Symmetry in Polygons

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Types of polygons A polygon is either concave or convex

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. A polygon is named for the number of sides 3triangle 4quadrilateral 5pentagon 6hexagon 7heptagon 8octagon 9nonagon 10decagon 12dodecagon

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 1) Draw an equilateral octagon

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms 3.1 Symmetry in Polygons An equiangular polygon is one in which all angles are congruent An equilateral polygon is one in which all sides are congruent A regular polygon is one that is both equianglular and equilateral.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 3.1 Symmetry in Polygons Classifications Triangles are Classified by the Number of Congruent Sides Three congruent sides At least two congruent sides No congruent sides equilateral isosceles scalene

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key skills 2. Is an equilateral triangle Isosceles?

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 3) Draw an isosceles right triangle

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 3.1 Symmetry in Polygons Definitions Reflectional Symmetry: A figure has reflectional symmetry if and only if its reflected image across a line coincides exactly with the preimage. The line is called an axis of symmetry. 4) Find the reflectional axis of symmetry of: TEO

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills 3.1 Symmetry in Polygons 5) Identify reflectional symmetry

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 3.1 Symmetry in Polygons Definitions Rotational Symmetry: A figure has rotational symmetry if and only if it has at least one rotation image that coincides with the original image.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills 3.1 Symmetry in Polygons 6) Identify rotational symmetry The figure has 4-fold rotational symmetry. The image will coincide with the original figure after rotations of 90°, 180°, 270° and 360°.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Central Angle measure The measure of a central angle of a polygon with n sides is given by the following: 7) Find the central angle of a regular heptagon

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 3.1 Symmetry in Polygons 8) Find the central angle of a regular pentagon Conclusion: central angles of a regular polygon are congruent

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Assignment Practice 3-1 and Page 143 # 7,8,13,23- 31,46,50,55-58,65-68