SymmetryReflectionalRotational

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

REFLECTIONREFLECTION

REFLECTIONAL SYMMETRY

An easy way to understand reflectional symmetry is to think about folding.

Do you remember folding a piece of

paper, drawing half of a heart, and then

cutting it out?

What happens when you unfold the piece

of paper?

REFLECTIONAL SYMMETRY

The two halves make a whole heart.

The two halves are exactly the same…

They are symmetrical.

Reflectional Symmetry

means that a shape can be folded along a line of reflection so

the two halves of the figure match exactly,

point by point.

The line of reflection in a figure with

reflectional symmetry is called a

line of symmetry.

Line of Symmetry

REFLECTIONAL SYMMETRYThe line created by the fold is the line of symmetry.

A shape can have more than one line of symmetry.

Where is the line of symmetry for this shape?How can I fold this shape so

that it matches exactly?

NOT THIS WAY

I CAN THIS WAY

Line of Symmetry

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

REFLECTIONAL SYMMETRYHow many lines of symmetry does each regular shape have?

Do you see a pattern?

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Infinite lines of symmetry

What is true for every line of symmetry?

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

What about a circle?

REFLECTIONAL SYMMETRYWhich of these flags have reflectional symmetry?

United States of America

Mexico

Canada

England

ROTATIONAL SYMMETRYA shape has rotational symmetry if, after you rotate less than one full turn, it is the

same as the original shape.Here is an example…As this shape is rotated 360, is it ever

the same before the shape returns to its original direction?

Yes, when it is rotated 90 it is the same as it was in the beginning.

What other angles make it look like the original?

90G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

180 270

ROTATIONAL SYMMETRY

Here is another example…As this shape is rotated 360, is it ever the same before the shape returns to

its original direction?

Yes, when it is rotated 180 it is the same as it was in the beginning.

So this shape is said to have rotational symmetry.180

A shape has rotational symmetry if, after you rotate less than one full turn, it is the

same as the original shape.

ROTATIONAL SYMMETRY

Here is another example…As this shape is rotated 360, is it ever the same before the shape returns to

its original direction?

No, when it is rotated 360 it is never the same.

So this shape does NOT have rotational symmetry.

A shape has rotational symmetry if, after you rotate less than one full turn, it is the

same as the original shape.

ROTATION SYMMETRYDoes this shape have rotational symmetry?

120

Yes, when the shape is rotated 120 it is the

same. Since 120 is less than 360, this shape

HAS rotational symmetry.

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

240 Notice we can also rotate 240 and have the same figure.

ROTATION SYMMETRYDoes this shape have rotational symmetry?

Yes, when the shape is rotated any number of

degrees, it is the same. This shape

HAS rotational symmetry.

WHAT KINDS OF SYMMETRY?

Reflectional: 3 lines of symmetryRotational: 120° and 240°

WHAT KINDS OF SYMMETRY?

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Propeller #1 Propeller #2Reflectional (5 lines of symmetry)Rotational (360/5 = 72°)

Rotational (72°) only

WHAT KINDS OF SYMMETRY?

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

WHAT KINDS OF SYMMETRY?

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

WHAT KINDS OF SYMMETRY?

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Homework

pp. 621-624 (2-9, 13-15, 27-33)

G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.