Symmetry Rotation Translation Reflection

Symmetry

What is a line of symmetry? A line on which a figure can be folded so that both sides match.

To be a line of symmetry, the shape must have two halves that match exactly. When you trace a heart onto a piece of folded paper, and then cut it out, the two half hearts make a whole heart. The two halves are symmetrical.

Which of these flags have a line of symmetry? United States of America Canada No Maryland England No

What about these math symbols? Do they have symmetry? + - Yes Yes - x Yes Yes

How many lines of symmetry to these regular polygons have? 5 4 3 Do you see a pattern? 6 8

A B C D E FG H I J K L M N O P Q R S T U V W X Y Z You can look to see if your name has symmetrical letters in it too! A B C D E FG H I J K L M N O P Q R S T U V W X Y Z Infinite number

The action of turning a figure around a point or a vertex. Rotation (Turn) The action of turning a figure around a point or a vertex.

Rotation Click the triangle to see rotation Turning a figure around a point or a vertex Rotation

If a shape spins 360, how far does it spin? ROTATION If a shape spins 360, how far does it spin? 360 All the way around This is called one full turn.

Half of the way around ROTATION If a shape spins 180, how far does it spin? Rotating a shape 180 turns a shape upside down. Half of the way around 180 This is called a ½ turn.

If a shape spins 90, how far does it spin? ROTATION If a shape spins 90, how far does it spin? One-quarter of the way around 90 This is called a ¼ turn.

ROTATION Describe how the triangle A was transformed to make triangle B A B Triangle A was rotated right 90 Describe the translation.

ROTATION Describe how the arrow A was transformed to make arrow B B A Arrow A was rotated right 180 Describe the translation.

The action of sliding a figure in any direction. Translation (Slide) The action of sliding a figure in any direction.

A TRANSLATION IS A CHANGE IN LOCATION. In geometry, a transformation is a way to change the position of a figure. With translation all points of a figure move the same distance and the same direction. A TRANSLATION IS A CHANGE IN LOCATION.

TRANSLATION In the example below triangle A is translated to become triangle B. A B Triangle A is slide directly to the right. Describe the translation.

TRANSLATION In the example below arrow A is translated to become arrow B. A B Arrow A is slide down and to the right. Describe the translation.

Click the Octagon to see Translation. The act of sliding a figure in any direction.

R E F L E C T I O N

The result of a figure flipped over a line. Reflection (flip) The result of a figure flipped over a line.

A REFLECTION IS FLIPPED OVER A LINE. A reflection is a transformation that flips a figure across a line. A REFLECTION IS FLIPPED OVER A LINE.

A REFLECTION IS FLIPPED OVER A LINE. The line that a shape is flipped over is called a line of reflection. Line of reflection A REFLECTION IS FLIPPED OVER A LINE.

Reflection Click on this trapezoid to see reflection. The result of a figure flipped over a line.

REFLECTIONAL SYMMETRY The line created by the fold is the line of symmetry. How can I fold this shape so that it matches exactly? A shape can have more than one line of symmetry. Where is the line of symmetry for this shape? I CAN THIS WAY NOT THIS WAY Line of Symmetry

Which shapes show reflection, translation, or rotation?

CONCLUSION FLIP REFLECTION SLIDE TRANSLATION TURN ROTATION We just discussed three types of transformations. See if you can match the action with the appropriate transformation. FLIP REFLECTION SLIDE TRANSLATION TURN ROTATION