Unit 7: Similarity

Unit 7 Learning Targets 

LT7-1: I can perform a dilation.

LT7-2: I can prove 2 figures are similar.

LT7-3: I can determine 2 triangles similar using shortcuts.

LT7-4: I can use similarity to find missing lengths in overlapping triangles.

LESSON 7-1

Dilations

A dilation is a transformation that preserves angle measure but not length. The dilation of a figure is determined by the scale factor and center of dilation. Every distance from the center of dilation and every side length in a preimage are multiplied by the scale factor to find the corresponding distance and side length in the image.

Help Videos:

●       How Do You Solve a Scale Model Problem Using a Scale Factor?

●       How Do You Find a Scale Factor in Similar Figures?

Practice:

6-1 Math XL

LESSON 7-2

Similarity Transformations

A similarity transformation is a dilation combined with one or more rigid motions. In order for two figures to be similar, there must be a similarity transformation that maps one figure to the other. All circles are similar.

Help Videos:

●       How Do You Graph a Translation Then a Dilation?

●       How Do You Identify a Similarity Transformation?

Practice:

7-2 Math XL

LESSON 7-3

Proving Triangles Similar

Two triangles are similar if a composition of rigid motions and dilation will map one triangle onto the other. Two pairs of congruent angles, or three pairs of sides with lengths that are in the same proportion, or two pairs of sides having congruent included angles with lengths that are in the same proportion, are sufficient to show that two triangles are similar.

Help Videos:

●       How Do You Determine If Two Triangles Are Similar Using the SAS Similarity Postulate?

●       How Do You Determine If Two Triangles Are Similar Using the AA Similarity Postulate?

Practice:

7-3 Math XL

LESSON 7-4

Similarity in Right Triangles

The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments into which the altitude divides the hypotenuse. The length of a leg of a right triangle is the geometric mean of the length of the hypotenuse and the segment of the hypotenuse adjacent to the leg.

Help Videos:

●       What Is a Geometric Mean?

●       How Do You Find a Geometric Mean?

Practice:

7-4 Math XL

Unit 7 Vocabulary

●       dilation 

●       similarity transformation 

●       geometric mean