Post on 05-Jan-2016
description
Stretching and Shrinking
SIMILAR FIGURES
Unit Test Review
100
200
300
400
500
100
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500
100
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400
500
Enlarging & Reducing
Shapes
SimilarFigures
SimilarPolygons
Similarity & Ratios
100
200
300
400
500
Vocabulary
100
200
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400
500
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.
Vocabulary - 500Vocabulary - 500
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Adjacent is the sides that are touching.
Investigation 1 - 100Investigation 1 - 100
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What is 10% of 80?
Inv. 1 Answer - 100Inv. 1 Answer - 100
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10% of 80 = 8
Investigation 1 - 200Investigation 1 - 200
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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.
Investigation 1 - 300Investigation 1 - 300
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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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Investigation 1 - 400Investigation 1 - 400
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Inv. 1 Answer - 400Inv. 1 Answer - 400
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Investigation 1 - 500Investigation 1 - 500
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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.
Investigation 2 - 100Investigation 2 - 100
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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.
Inv. 2 Answer - 100Inv. 2 Answer - 100
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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!
Investigation 2 - 200Investigation 2 - 200
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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.
Inv. 2 Answer - 200Inv. 2 Answer - 200
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Answers may vary.
Investigation 2 - 300Investigation 2 - 300
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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
Inv. 2 Answer - 300Inv. 2 Answer - 300
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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
Inv. 2 Answer - 400Inv. 2 Answer - 400
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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.
Inv. 2 Answer - 500Inv. 2 Answer - 500
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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?
Inv. 3 Answer - 100Inv. 3 Answer - 100
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The scale factor is 5.
Investigation 3 - 200Investigation 3 - 200
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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
Inv. 3 Answer - 200Inv. 3 Answer - 200
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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
Inv. 3 Answer - 300Inv. 3 Answer - 300
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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.
Investigation 3 - 400Investigation 3 - 400
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50°
T
What is the measure of angle T?
Inv. 3 Answer - 400Inv. 3 Answer - 400
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50°
T
T = 40°
90° + 50° = 140°
180° – 140° = 40°
Investigation 3 - 500Investigation 3 - 500
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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.
Inv. 3 Answer – 500Inv. 3 Answer – 500
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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
Investigation 4 - 100Investigation 4 - 100
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Inv. 4 Answer - 100Inv. 4 Answer - 100
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Investigation 4 - 200Investigation 4 - 200
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Inv. 4 Answer - 200Inv. 4 Answer - 200
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Investigation 4 - 300Investigation 4 - 300
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Inv. 4 Answer - 300Inv. 4 Answer - 300
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Investigation 4 - 400Investigation 4 - 400
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Inv. 4 Answer - 400Inv. 4 Answer - 400
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Investigation 4 - 500Investigation 4 - 500
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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
Inv. 4 Answer - 500Inv. 4 Answer - 500
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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.