CONFIDENTIAL 1

Good Afternoon!

Today we will be learning about Similarity and Symmetry

Let’s warm up :

Write Reflection, Rotation or Translation to describe how the figure was moved:

1) 2)

3) 4)

1) Reflection, Translation 2) Rotation

3) Rotation 4) Reflection

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If one shape can become another using Turns, Flips and/or Slides, then the two shapes are called

Congruent:

The three main Transformations are:

Reflection : Flip!

Rotation : Turn!

Translation : Slide!

After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and

line lengths.

Let’s review what we did in the last session

We learnt about transformation .

CONFIDENTIAL 3

The central line is called the Mirror Line, and it doesn't matter what direction the mirror line goes, the

reflected image is always the same size, it just faces the other way.

A reflection over a line, is a transformation in which each point of the original figure (pre-image) has an

image that is the same distance from the line of reflection as the original point but is on the opposite

side.

Reflection

Review

CONFIDENTIAL 4

You can try reflecting different shapes about different mirror lines.

Just approach it step-by-step. For each corner of the shape:

Measure from the point to the mirror line (must hit the mirror line at a right angle)

Step1

Reflection

Review

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Measure the same distance again on the other side and place a dot.

Then connect the new dots up!

Step2

Step3

Reflection

Review

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It is common to label each corner with letters, and to use a little dash (called a

Prime) to mark each corner of the reflected image.

Here the original is ABC and the reflected image is A'B'C'

Labels

Review

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Rotation

When we "rotate" an object round a point.

The distance from the center to any point on the shape stays the same! and

Every point makes a circle around the center.!

We can notice that

"Rotation" means turning around a center.

Review

CONFIDENTIAL 8

A rotation is a transformation, that moves every point around a fixed point (usually the origin).

Rotation

A rotation creates a figure that is congruent to the original figure and preserves distance and

orientation .

Review

CONFIDENTIAL 9

Review

Translation

In Geometry, "Translation" simply means Moving .. without rotating, resizing or anything else, just

moving.Every point of the shape must move:

* the same distance

* in the same direction.

A translation is a transformation that slides every point of a figure the same distance in the same

direction.

CONFIDENTIAL 10

Let’s start withSimilarity and

Symmetry

Similar: Two shapes are Similar if the only difference is size.

If one shape can become another using Resizing, then the shapes are Similar.

Example:

When two shapes are similar, then:

corresponding angles are equal, and the lines are in proportion.

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Resized Resized

and Reflected

Resized and

Rotated

These shapes are all Similar.

Sometimes it can be hard to see if two shapes are Similar, because you may need to turn, flip or slide one shape as well as resizing it.

If one shape can become another using Resizing, then the shapes are Similar.

CONFIDENTIAL 12

Fold this picture in half. The two parts match exactly. This picture has

“symmetry.”

Where you fold the shape, or the fold line, is called the line of symmetry.

Line of symmetry

Symmetry: When a picture or figure has symmetry, it can be folded in half so that the two parts match exactly.

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Line Symmetry

A figure has line symmetry if it can be folded in half so that the two halves match exactly i.e. one

halfof it is the mirror image of the other half.

Line symmetry is also called bilateral symmetry.

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Figures can have any number of lines of symmetry, from no lines of symmetry to an

infinite, or unlimited, number of lines of symmetry.

No lines of

symmetry

One line of

symmetry

Two lines of

symmetry

Infinite lines of symmetry

The Line Symmetry is sometimes called Reflection Symmetry or Mirror Symmetry.

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Rotational Symmetry

With rotational Symmetry, the shape or image can be rotated clockwise or counterclockwise 180°and it still

looks the same.

Rotational Symmetry: A figure has rotational symmetry if it can be rotated about a point less than a

full turn to make the figure look the same as it did before the rotation.

Quarter turn

Half turn

3-Quarter turn

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Point Symmetry

Point Symmetry: is when every part has a matching part.

* the same distance from the central point

* but in the opposite direction.

Point Symmetry is sometimes called Origin Symmetry, because the "Origin" is the central point about which the shape is

symmetrical.

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Same from Opposite Direction?

Yes, pick a direction, and anything with Point Symmetry will look the same from the opposite

direction, too.

These Letters have Point Symmetry, too!

It looks the same Upside Down!

(... or from any two opposite directions*)

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Symmetry exists all around us

You can find symmetry in nature, architecture and art.

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BREAK

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GAME

Click on the link below for some exciting puzzle

http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsaw-puzzles/12-piece-jigsaw/11-07-06-snowprincess.html

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Assignments

Write whether of figures are similar or not:

1) 2)

3)

4)5)

2) Not Similar 1) Similar 1) Similar

3) Similar

4) Not Similar 5) Similar

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Is the dotted line a line of symmetry:

6)

8)

7)

9) 10)

6) yes 7) no

8) yes

9) yes 10) no

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Very Good!Let's Review

Similar: Two shapes are Similar if the only difference is size.

If one shape can become another using Resizing, then the shapes are Similar.

Example:

When two shapes are similar, then:

corresponding angles are equal, and the lines are in proportion.

CONFIDENTIAL 24

Review

Resized Resized

and Reflected

Resized and

Rotated

These shapes are all Similar.

Sometimes it can be hard to see if two shapes are Similar, because you may need to turn, flip or slide one shape as well as resizing it.

If one shape can become another using Resizing, then the shapes are Similar.

CONFIDENTIAL 25

Review

Fold this picture in half. The two parts match exactly. This picture has

“symmetry.”

Where you fold the shape, or the fold line, is called the line of symmetry.

Line of symmetry

Symmetry: When a picture or figure has symmetry, it can be folded in half so that the two parts match exactly.

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Review

Line Symmetry

A figure has line symmetry if it can be folded in half so that the two halves match exactly i.e. one

halfof it is the mirror image of the other half.

Line symmetry is also called bilateral symmetry.

CONFIDENTIAL 27

ReviewFigures can have any number of lines of

symmetry, from no lines of symmetry to an infinite, or unlimited, number of lines of

symmetry.

No lines of

symmetry

One line of

symmetry

Two lines of

symmetry

Infinite lines of symmetry

The Line Symmetry is sometimes called Reflection Symmetry or Mirror Symmetry.

CONFIDENTIAL 28

Review

Rotational Symmetry

With rotational Symmetry, the shape or image can be rotated clockwise or counterclockwise 180°and it still

looks the same.

Rotational Symmetry: A figure has rotational symmetry if it can be rotated about a point less than a

full turn to make the figure look the same as it did before the rotation.

Quarter turn

Half turn

3-Quarter turn

CONFIDENTIAL 29

Review

Point Symmetry

Point Symmetry: is when every part has a matching part.

* the same distance from the central point

* but in the opposite direction.

Point Symmetry is sometimes called Origin Symmetry, because the "Origin" is the central point about which the shape is

symmetrical.

CONFIDENTIAL 30

Review

Same from Opposite Direction?Yes, pick a direction, and anything with Point

Symmetry will look the same from the opposite direction, too.

These Letters have Point Symmetry, too!

It looks the same Upside Down!

(... or from any two opposite directions*)

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Symmetry exists all around us

You can find symmetry in nature, architecture and art.

Review

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You have done a nice job.See you in the next session.