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B E F 30 ° 45° 60 ° 45° A D C. Name a ray that bisects AC or

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### 3.1 Symmetry in Polygons

E F

30°

45°

60° 45°

A D C

Name a ray that bisects AC

or

Name the perpendicular bisector of AC

or

Name the bisector of <CDB

or

BD

DB

BD

DF

BD

DF

Geometry warm upD is the midpoint of AC

When you get done with this, please make a new note book

What is symmetry?

There are two types we’re concerned with:

Rotational and Reflective

If a figure has ROTATIONAL symmetry, then you can rotate it about a center and it will match itself (don’t consider 0° or 360°)

If a figure has REFLECTIONAL symmetry, it will reflect across an axis.

What are polygons?

A plane figure formed by 3 or more segments

Has straight sides

Sides intersect at vertices

Only 2 sides intersect at any vertex

It is a closed figure

Polygons are named by the number of sides they have:

Names of polygonsVocabulary

- Equiangular – All angles are congruent
- Equilateral – All sides are congruent
- Regular (polygon) – All angles have the same measure AND all sides are congruent
- Reflectional Symmetry – A figure can be cut in half and reflected across an axis of symmetry.
- Rotational Symmetry – A figure has rotational symmetry iff it has at least one rotational image (not 0° or 360°) that coincides with the original image.

Central

angle

EQUILATERAL triangle has 3 congruent sides

ISOCELES triangle has at least 2 congruent sides

SCALENE triangle has 0 congruent sides

Center – in a regular polygon, this is the point equidistant from all vertices

Central Angle – An angle whose vertex is the center of the polygon

A little more vocabC

Activities

- 3.1 Activities 1- 2 (hand out)
- Turn it in with your homework

What you should have learned about Reflectional symmetry in regular polygons

- When the number of sides is even, the axis of symmetry goes through 2 vertices
- When the number of sides is odd, the axis of symmetry goes through one vertex and is a perpendicular bisector on the opposite side

What you should have learned about rotational symmetry

- To find the measure of the central angle, theta, θ, of a regular polygon, divide 360° by the number of sides. 360/n = theta
- To find the measure of theta in other shapes, ask: “when I rotate the shape, how many times does it land on top of the original?”
- Something with 180° symmetry would have 2-fold rotational symmetry
- Something with 90 degree rotational symmetry would be 4-fold

Homework

- Practice 3.1 A, B & C worksheets

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