Welcome to class.Please pick up and complete a pink warm up

from the back table.

Turn in your signed progress reports for $10.

Warm up

3.1.1 – Similarity & Dilation3.1.2 – Proportional Growth and

Ratios

Dilation – a non-rigid transformation that changes the size of a figure while maintaining its shape. The result is a similar figure.

3.1.1 – Dilation

Stretching is NOT dilating

To dilate a figure: 1. Start from the point of

dilation2. Dilate each vertex by the

scale factor, making a dot at each new point.

3. Connect the new vertices.4. Be sure to label the pre-

image and image appropriately.

This figure has a scale factor of 3.

Notice that the distance between the point of dilation and the vertex can be different for each vertex.

A scale factor > 1 ENLARGES the shape

A scale factor < 1 REDUCES the shape

3

1

2

B’

Get:ONE partner

Resource page 3.1.1 (one per team)scissors (one per team)

straight edge (one per team)

I will number you off…

#1s will dilate the shape by a factor of 2#2s will dilate the shape by a factor of 3#3s will dilate the shape by a factor of 4#4s will dilate the shape by a factor of 5

Distance formulaPut this in your notes!!Given 2 points (x1, y1) and (x2, y2)

D = √(x2 – x1)2 + (y2 – y1)2

Given 2 points (3, 4) and (0, -2)d = √(0 – 3)2 + (-2 – 4)2

d = √(-3) 2 + (-6) 2

d = √9 + 36d = √45d = 3√5

In order for shapes to be similar, they have to be changed by the same

RATIO

2

6

6

18

Notice that the image was changed by a ratio of 3 (or 3/1) from the pre-image.

Pre-image

Image

Are these 2 shapes SIMILAR?

Check the ratio of the sides:If the corresponding sides are in the same ratio, then the

shapes are similar

17 5325

3618

34

17 = 1

34 2

25 = 25

53 53 18 = 1

36 2

Then you have to set up a PROPORTION

5

x

3.5

17

5 = 3.5

17 x

Cross products:

5x = 59.9

X = 11.9

5 = 17

3.5 x

Cross products: (notice how they are the same?)

5x = 59.9

X = 11.9

Your assignment

Pg 138 – 143; 5-9, 17-21, not 8c