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MathScience Innovation Center © 2007

Similarity

Similar figures have the same shape but not necessarily the same size.


Tests for Similarity• The measures of their

corresponding angles are equal.• The lengths of their corresponding

sides increase by the same scale factor.


Each of the shapes below have five sides and 5 angles, but which shape is similar to Z?

Choic

e O

ne

Choic

e Two

Choic

e Thre

e

0% 0%0%

1. Choice One2. Choice Two3. Choice Three

A

B

Z

Question 1 - Review


Triangle RST is an enlargement of triangle WXY. Which answer choice lists a pair of corresponding sides?

RS a

nd WY

RT a

nd XW

ST a

nd XY

ST a

nd YW

0% 0%0%0%

1. RS and WY2. RT and XW3. ST and XY4. ST and YW

S

R T W

X

Y

Question 2- Review


Triangle RST is an enlargement of triangle WXY. Which answer choice lists a pair of corresponding angles?

1. and2. and3. and4. and

RST

an

d

an

d

an

d

an

d

0% 0%0%0%

XWY

RTS XWY

STR XYW

SRT WYX

W

X

Y

R T

S

Question 3 - Review


Question 4 - Review

If two figures are similar, which of the following might be different?

0%

0%

0%

0% a. number of sidesb. shapec. size of anglesd. area


Activity 1

The first shape is a self-similar shape and the second is not. What do you think a self-similar shape is?


Question 1 – Activity 1

Is the number of copies of an original shape used to make a new shape related to the side lengths or the area of the new shape?

0%

0% 1. Side lengths

2. Area of new shape

MathScience Innovation Center © 2007 Yes N

o

0%0%1. Yes2. No


Quad 1 Quad 2

Are these two quadrilaterals mathematically similar?


Can the larger shape be divided into smaller congruent shapes that are similar to the original?

Yes N

o

0%0%

1. Yes2. No



YES


Question 1 – Activity 2What can be said about the angles of similar figures

0%

0%

0% 1. The angles are different.

2. The angles are the same.

3. The angles change by 180°.



Yes N

o

0%0%

1. Yes2. No

Does the concept of similarity apply to three dimensional shapes?

Scale Models


Shrinking Cups

What would happen if you were smaller?

What challenges would you face if were much smaller, only inches tall?


Shrinking Cups

What challenges would you face if you had to design a cup to drink from if you were only 6-12 inches tall?

Would we have to consider any aspects other than size?

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