Welcome to class. Please pick up and complete a pink warm up from the back table. Turn in your...
-
Upload
mark-wells -
Category
Documents
-
view
214 -
download
0
Transcript of Welcome to class. Please pick up and complete a pink warm up from the back table. Turn in your...
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 + 36
d = √45
d = 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