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Lesson 8.7, For use with pages 439-444
Tell whether the figure is a reflection in the line shown?
1. 2.
Lesson 8.7, For use with pages 439-444
Tell whether the figure is a reflection in the line shown?
ANSWER no
1.
ANSWER yes
2.
8.8 Similarity and Dilations
Essential Questions
• What are the similarities and differences among transformations?
• How are the principles of transformational geometry used in art, architecture and fashion?
• What are the applications for transformations?
Similar Polygons
• Similar polygons have the same shape but can be different sizes. The symbol ~ means “is similar to.”
EXAMPLE 1 Identifying Similar Polygons
STEP 1
Decide whether corresponding angles are congruent. Each angle measures 90.
Tell whether the television screens are similar.
A E B F
C G D H
STEP 2Decide whether corresponding side lengths are proportional.
EXAMPLE 1 Identifying Similar Polygons
30 inches18 inches
40 inches24 inches=?
53
= 53
ANSWER
Yes, quadrilateral ABCD ~ quadrilateral EFGH.
SOLUTION
EXAMPLE 2 Standardized Test Practice
Corresponding side lengths are proportional.KLNP
= LMPQ
KL12M
= 10M5M
KL = 24
Write a proportion.
Substitute given values.
Solve the proportion.
EXAMPLE 3 Using Indirect Measurement
Height
Alma is 5 feet tall and casts a 7 foot shadow. At the same time, a tree casts a 14 foot shadow. The triangles formed are similar. Find the height of the tree.
SOLUTION
EXAMPLE 3 Using Indirect Measurement
You can use a proportion to find the height of the tree.
Tree’s heightAlma’s height
=Length of tree’s shadow
Length of Alma’s shadowWrite a proportion.
Substitute given values.x feet5 feet =
14feet7 feet
x 10= Solve the proportion.
ANSWER
The tree is 10 feet tall.
Dilation
• Stretches or shrinks a figure
• The image created by a dilation is similar to the original figure.
• Scale factor: of a dilation is the ratio of a side length after the dilation to the corresponding side length before the dilation.
Dilations
• National Library of Virtual Manipulatives – Geometry 6-8– Transformations- Dilations
• Dimensions can be scaled “UP” or scaled “DOWN” – as stated before.
• To scale up, means you would multiply by a number that is _______________.
• To scale down, you would multiply by a number that is _________________
greater than one.
less than one
EXAMPLE 4 Dilating a Polygon
Quadrilateral ABCD has vertices A(– 1, – 1), B(0, 1), C (2, 2), and D(3, 0). Dilate using a scale factor of 3.
SOLUTION
Original Image(x, y)
A(–1, –1)B(0, 1)C(2, 2)D(3, 0)
(3x, 3y)A’(– 3, – 3)B’(0, 3)C’(6, 6)D’(9, 0)
EXAMPLE 4 Dilating a Polygon
Quadrilateral ABCD has vertices A(– 1, – 1), B(0, 1), C (2, 2), and D(3, 0). Dilate using a scale factor of 3.
SOLUTION
Graph the quadrilateral. Find the coordinates of the vertices of the image.
Original Image(x, y)
A(–1, –1)B(0, 1)C(2, 2)D(3, 0)Graph the image of the quadrilateral.
(3x, 3y)A’(– 3, – 3)B’(0, 3)C’(6, 6)D’(9, 0)
1. Graph the polygon with vertices V(0, 0), W(–4, –6), and X(4, –2). Dilate by the scale factor , and graph the image.
1
2
ANSWER
Homework
• Page 450 #1-8, 12, 14
– Number 12: D (2,6)
– Number 14: k =2