8.8 similarity and dilations 1

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