Unit 6 Lesson 6.4: Proportional Relationships

Unit 6 Lesson 6.4: Proportional Relationships

MT: Using Transformations to Prove Similarity

RECALL:

PROPERTIES OF SIMILARITY

RECALL:

PROPORTIONS

A proportion is when two or more ratios have the same value.

​

You only need AT LEAST two ratios to create a proportion. ​

NOTE:

DISTRIBUTIVE PROPERTY

PRACTICE:

​Given that two figures are similar, find the values of x and y using the properties of congruence and proportions.

PRACTICE:

x = 17​

PRACTICE:

​Given that two figures are similar, find the values of x and y using the properties of congruence and proportions.

PRACTICE:

PRACTICE:

How the BUTTERFLY METHOD works:  

 

 

 ​

PRACTICE:

y = 5​

Multiple Choice

Given that the two figures

( $$JKLMN\ \&\ VWXYZ$$ ) are similar, find the values of x and y.

• x=25

  y=1

• x=5

  y=1

• x=5

  y=7

• x=25

  y=7

Multiple Choice

Find the height of the palm tree, AB, using the properties of similarity.

• 11.52

• 0.2

• 4.5

• 8.8

Multiple Choice

Sid is 72 inches tall. To measure a flagpole, Sid stands near the flag. Sid’s friend Miranda measures the lengths of Sid’s shadow and the flagpole’s shadow. Find the height h of the flagpole.

• 85 in.

• 27 in.

• 192 in.

Multiple Choice

To find the distance d across the gorge, a student identifies points as shown in the figure. Find d.

• 20 m

• 61.25 m

• 28.8 m

Multiple Choice

Given that the two figures ( $$\Delta ADC\ \&\ \Delta AEB$$ )  are similar, find the values of x and y.

• x=12

  y=7

• x=12

  y=1.4

• x=21.3

  y=7

• x=21.3

  y=1.4