Recognize Determine Identify - Edgenuity Inc.

Warm-Up Similarity and Transformations

?

Lesson

Question

Lesson Goals

Recognize

figures.

Determine similar figures through .

Identify and describe transformations that create similar figures.

W2K

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you.

a multiplicative factor used to stretch or shrink a figure or drawing

a pair of angles that have the same relative position in two congruent figures

a transformation that changes the size but not the shape of a figure

an operation on a figure that may change its location in a plane, orientation, or shape

figures that have corresponding angles that are congruent and corresponding side lengths that are in proportion

a pair of sides that have the same relative position in two congruent figures

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Warm-Up Similarity and Transformations

Dilations

2 A A 2

P

B C B

C

? A dilation changes the size of a

.

? An enlargement

its size.

? A reduction decreases its size.

? The scale factor measures how much larger or

the image is.

? Scale factor tells us how the

compares to the pre-image.

PA = PA

Note that the sides of the triangle ABC are all double the length of the sides of triangle ABC.

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Instruction Similarity and Transformations

Slide

2

Similar Figures

Similar figures are the same .

, but not necessarily the same

All the angles of the squares are congruent and the side lengths are proportional.

The corresponding angles of the triangles are all congruent. And the side lengths are all proportional.

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Instruction Similarity and Transformations

Slide

3

Similarity of Triangles

Given the two triangles, determine if the figures are similar.

yA 4

C

2

-6 -4 -2 angle 33.7 -2

B

x

24 D

-4 F

E

-6

Measure the corresponding angles:

mF = 33.7? = m mE = 90? = m mD = 56.3? = m

Measure the corresponding sides. CB 6 = =2 FE 3 AB = 4 = 2 DE 2 CA 7.2 = =2 FD 3.6

So, corresponding angles are

So, corresponding sides are

.

, and the scale

factor is either 2 or 1. 2

Since I know that corresponding angles are congruent and that corresponding

sides are congruent, I know that triangle ACB is

to triangle DFE.

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Instruction Similarity and Transformations

Slide

5

Determining Similarity

EXAMPLE

Are the triangles similar?

3 cm

3 cm

2 cm

4.5 cm

4.5 cm

3 cm I can see by the notation in the angles that all the corresponding angles are

.

= 1.5

3 3

= 1.5

The scale factor is

.

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