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

Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

Section 3-1 Symmetry

3.1 Symmetry in Polygons


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.



Types of polygons• A polygon is either concave or convex


A polygon is named for the number of sides3 triangle

4 quadrilateral

5 pentagon

6 hexagon

7 heptagon

8 octagon

9 nonagon

10decagon

12dodecagon


1) Draw an equilateral octagon


Glossary Terms


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.



ClassificationsTriangles are Classified by the Number of Congruent Sides

Three congruent sides

At least two congruent sides

No congruent sides

equilateral

isosceles

scalene


Key skills

2. Is an equilateral triangle Isosceles?


3) Draw an isosceles right triangle



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:

T E O


Key Skills


5) Identify reflectional symmetry



DefinitionsRotational Symmetry: A figure has rotational symmetry if and only if it has at least one rotation image that coincides with the original image.


Key Skills


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°.


Central Angle measureThe 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



8) Find the central angle of a regular pentagon

Conclusion: central angles of a regular polygon are congruent


AssignmentPractice 3-1 and Page 143 # 7,8,13,23-

31,46,50,55-58,65-68

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

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