Stretching and Shrinking

SIMILAR FIGURES

Unit Test Review

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Enlarging & Reducing

Shapes

SimilarFigures

SimilarPolygons

Similarity & Ratios

100

200

300

400

500

Vocabulary

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Vocabulary - 100Vocabulary - 100

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Define Similar

Vocabulary - 100Vocabulary - 100

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Same shape, but not the same size.

Vocabulary - 200Vocabulary - 200

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Draw 2 figures and color code their corresponding

sides

Vocabulary - 200Vocabulary - 200

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The side in the same relative position on a

similar figure.

Vocabulary - 300Vocabulary - 300

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Define Scale Factor

Vocabulary - 300Vocabulary - 300

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The number used to multiply the lengths of a figure to stretch or

shrink it to a similar image.

Vocabulary - 400Vocabulary - 400

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Give an example of equivalent ratios.

Vocabulary - 400Vocabulary - 400

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Ratios whose fraction representation are the same.

Vocabulary - 500Vocabulary - 500

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Draw 2 rectangles and color code the

adjacent sides.

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Adjacent is the sides that are touching.

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What is 10% of 80?

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10% of 80 = 8

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If a three-band stretcher is used to enlarge a rectangle, how will the perimeter of the enlargement compare to the perimeter of the original?

Inv. 1 Answer - 200Inv. 1 Answer - 200

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The perimeter of the enlargement will be three times larger than the original.

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If a three-band stretcher is used to enlarge a triangle, how will the angles of the enlargement compare to the angles of the original?

Inv. 1 Answer - 300

Corresponding angles of similar figures have the same measure.

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Inv. 1 Answer - 400Inv. 1 Answer - 400

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If a three-band stretcher is used to enlarge a triangle, how will the area of the enlargement compare to the area of the original?

Inv. 1 Answer - 500Inv. 1 Answer - 500

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The area of the enlargement will be 9 times larger.

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Suppose you used the rule (6x, 6y) to transform a figure into a new figure. How would the angles of the new figure compare with the angles of the original? Explain.

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The angles would be the same because 6 is being multiplied by the length and width. The two figures will be similar which makes their corresponding angles the same!

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Write a rule that can be applied to the length and width of a rectangle to create a figure that is not similar.

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Answers may vary.

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If you enlarge the rectangle below at a scale factor of 200%, what will the new dimensions be?

10 cm

4 cm

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20 cm

8 cm

Steps:•Convert 200% to decimal of 2.00•2 x 10 = 20 cm•2 x 4 = 8 cm

Investigation 2 - 400Investigation 2 - 400

(x, y) (2, 1) (6, 1) (4, 6)

(2x, y +1) (4, 2) (12, 1) (8, 7)

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Robert graphed a triangle on a coordinate plane. He decided to see what happened if he transformed the shape with the rule (2x, y+1). Which of the following tables could be an actual representation of his original triangle and his transformation? Explain.

A

(x, y) (2, 1) (6, 1) (4, 6)

(2x, y +1) (4, 2) (12, 2) (8, 7)

B

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B.

(x, y) (2, 1) (6, 1) (4, 6)

(2x, y +1) (4, 2) (12, 2) (8, 7)

Investigation 2 - 500Investigation 2 - 500

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Tim wants to create Dug, a friend to Mug on the coordinate plane. His rule for Dug in relation to Mug is (x+1, y+2). Which of the following statements best describes Dug?

A) Dug will be enlarged so he is 2 times as large as Mug.

B) Dug will not be similar to Mug.

C) Dug will be congruent to Mug, but moved 1 space to the right and 2 spaces above Mug.

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C) Dug will be congruent to Mug, but moved 1 space to the right and 2 spaces above Mug.

(x+1, y+2) does not change the size at all. Adding a number to x and y just moves the figure in the coordinate plane.

Investigation 3 - 100Investigation 3 - 100

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The quadrilaterals below are similar. What is the scale factor from the small quadrilateral to the large quadrilateral?

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The scale factor is 5.

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ABCD is similar to EFGH. What is the scale factor from rectangle ABCD to rectangle EFHG?

A B

CD

3 cm

E F

GH

6 cm

9 cm

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The scale factor is 2.6/3 = 2

A B

CD

3 cm

E F

GH

6 cm

9 cm

Investigation 3 - 300Investigation 3 - 300

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ABCD is similar to EFGH. What is the scale factor from rectangle EFHG to rectangle ABCD?

A B

CD

3 cm

E F

GH

6 cm

9 cm

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A B

CD

3 cm

E F

GH

6 cm

9 cm

The scale factor is ½.

3/6 = ½ . ½ is the reciprocal of 2/1.

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50°

T

What is the measure of angle T?

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50°

T

T = 40°

90° + 50° = 140°

180° – 140° = 40°

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A B

CD

3 cm

E F

GH

6 cm

9 cm

ABCD is similar to EFGH. How does the area of ABCD compare to EFGH? Explain.

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A B

CD

3 cm

E F

GH

6 cm

9 cm

The area is 4 times larger because it is the (scale factor)2 22 = 4

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8 cm

12 cm

4 cm

6

Find the adjacent side ratios to see which triangles are similar. What about their angles?

AB

C

5 cm

6 cm

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8 cm

12 cm

4 cm

6AB

C

5 cm

6 cm

Triangle Long Side Short Side Ratio

A 12 8 12/8 = 1.5

B 6 4 6/4 = 1.5

C 6 5 6/5 = 1.2

A & B are similar if their corresponding angles are the same measure.