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Geometry Section 7-1A Changing the Size of FiguresPage 462You will need a calculator with sin/cos/tan in 2 weeks.Freshmen - TI 30 XII S recommended. Around $15. You’ll need it for Alg. II.

Similar Figures:

Similar Figures-

Figures that have the same shape, but not necessarily the same size. Think enlargements or reductions.

Pg.462

These figures are similar. Same shape, but not the same size.

These are not similar. None of these have the same shape.

Similar Figures:

Scale Factor: the amount of enlargement or reduction needed to get one figure from another.

If the scale factor is greater than 1, the similar figure is an enlargement; if the scale factor is less than 1, it is a reduction.

Pg.462

Explore:

Enlarge the side lengths by a factor of 3.

Choose a side in the original figure. Identify the corresponding side in your enlarged version. What is the ratio between the 2 sides? Is it the same for other sets of corresponding sides?

Pg.463

31

Use your protractor to measure the corresponding sets of angles. What is their ratio?

11

Explore:

Enlarge the side lengths by a factor of 3.

Choose a side in the original figure. Identify the corresponding side in your enlarged version. What is the ratio between the 2 sides? Is it the same for other sets of corresponding sides?

Pg.463

31

Use your protractor to measure the corresponding sets of angles. What is their ratio?

The ratio of the lengths of two corresponding sides of similar figures is the similarity ratio.

11

Example:

DABC is similar to DXYZ.

z

Find the similarity ratio of DABC to DXYZ.

AB 5

XY 9

=

Pg.463

Find the similarity ratio of DXYZ to DABC .

XY 9

AB 5

=

Try It:

a. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the figure on the left to the figure on the right.

Similar

Pg.464

1/2

If similar, find the similarity ratio of the figure on the right to the figure on the left.

2/1

Try It:

b. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the figure on the left to the figure on the right.

Similar

Pg.464

3/1

If similar, find the similarity ratio of the figure on the right to the figure on the left.

1/3

Try It:

c. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the figure on the left to the figure on the right.

Pg.464

Not similar

Try It:

d. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the figure on the left to the figure on the right.

Similar;

1/3

Pg.464

If similar, find the similarity ratio of the figure on the right to the figure on the left.

3/1

Definition:

- Definition of similar:
- Two polygons are similar if and only if:
- Their corresponding angles are congruent and
- Their corresponding side lengths are proportional.

Pg.464

Reflect:

Suppose you enlarge or reduce a figure to make a similar figure.

What happens to the measure of each of the angles?

The angle measures stay the same.

What happens to the length of each line segment?

Pg.465

Side lengths are multiplied by the scale factor.

If Figure X is similar to Figure Y, how is the similarity ratio from X to Y related to the similarity ratio from Y to X?

They are reciprocals of each other.

Exercises:

If you reduce a 15cm x 20cm rectangle by using a scale factor of 3/5, what will the dimensions of the reduced rectangle be?

#4

Pg.465

35

15 x =

9

35

20 x =

12

9cm x 12cm

Exercises:

If you enlarge a 9 in x 12 in rectangle by using a scale factor of 2.5, what will the new dimensions be?

9 x 2.5 =

22.5

#5

Pg.465

12 x 2.5 =

30

22.5 in x 30 in

Exercises:

True or False?

Any 2 squares are similar.

True

#6, 7

Pg.466

Any 2 rectangles are similar.

False. The ratio of the lengths could be different from the ratio of the widths.

Exercises:

True or False?

Any 2 rhombuses are similar.

False. The sides remain in proportion, but the angles can be changed.

#8, 9

Pg.466

Any 2 equilateral triangles are similar.

True. All angles will be 60o and all sides will be proportional.

Exercises:

Each pair of figures is similar, and the length of corresponding sides are shown. Find the similarity ratio of Figure A to B and of B to A.

#12

Pg.466

A to B = 1/3

B to A = 3/1

Exercises:

State whether or not each pair of figures is similar. If similar, find the similarity ratio of the figure on the left to the figure on the right. If not similar, explain why.

#14

Pg.466

Not similar.

Sets of corresponding sides do not have the same ratio.

Exercises:

State whether or not each pair of figures is similar. If similar, find the similarity ratio of the figure on the left to the figure on the right. If not similar, explain why.

#15

Pg.466

Similar

2

3

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