Name: Period: Date:Unit 6: Ratios, Proportions, and Similarity Notes Packet #1 PACRS

BOA 20-23Solve routine two-step and three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and computing with a given average

M 33-36Use scale factors to determine the magnitude of a size change

CCSS

G-SRT.2 Given two figures use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Level 1 Objectives1. Students will be able to write ratios.

2. Students will be able to set up and solve proportions.

Directions: Find the specific ratio given a scenario.

1. A designated hitter made 10 hits in 15 games. Find the ratio of hits to games.

2. There are 80 boys in the sophomore class of 200 students. Find the ratio of boys to girls.

Example(s):Directions: Solve the following proportions.

1. 17.8

4=3.7

8 x =

2. = y =

3. = x =

1

4. = 8 a =

5. Sarah bought 32 kiwi for $16. How many can Lisa buy with 3 dollars?

6. Matt took a trip to Mexico. Upon leaving he decided to convert all of his Pesos back into dollars. How many dollars did he receive if he exchanged 42.7 Pesos at a rate of $5.30 = 11.1 Pesos?

Question: What is the difference between a ratio and a proportion?

Homework Level 1Worksheet

Level 2 Objectives1. Students will be able to identify similar figures.2. Students will be able to solve problems using scale factors.

2

3. Students will be able to solve word problems applying properties of proportions.

Similar Polygons:

Symbol for similarity:

Example:The order of the vertices in a similarity statement is important. It identifies the corresponding angles and the corresponding proportional sides.

Similarity statement Congruent angles Corresponding proportional sides

Directions: Determine whether the each pair of figures is similar. Justify your answer.

1.

2.

3.

3

Scale Factor:

In general:

Directions: The polygons in each pair are similar. Find the scale factor of the smallest figure to the larger figure.1.

2.

4

3.

Word Problems:

1. In a triangle, the ratio of the measures of three sides is 5:12:13, and the perimeter is 90 centimeters. Find the measure of the shortest side of the triangle.

2. The ratio of the measures of the three angles is 2:5:3. Find the measures of the angles of each triangle.

3. A twinjet airplane has a length of 78 meters and a wingspan of 90 meters. A toy model is made in proportion to the real airplane. If the wingspan of the toy is 36 centimeters, find the length of the toy.

4. Triangle ABC is similar to triangle XYZ with a scale factor of 2:3. If the lengths of the sides of triangle ABC are 5

6, 8, and 10 inches, what are the lengths of the sides of triangle XYZ?

5. The two polygons are similar. Write a similarity statement, find x, y and UT. Find the scale factor of polygon RSTUV and polygon ABCDE.

Homework Level 2Worksheet

Section 1.3 Level 3 Objectives

6

Students will be able to determine if two triangles are similar.Students will be able to identify and find parts of similar triangles.

There are three ways to determine whether two triangles are similar.Angle-Angle Similarity:(AA Similarity)

Side-Side-Side Similarity:(SSS Similarity)

Side-Angle SideSimilarity:(SAS Similarity)

Directions: Determine whether each pair of triangles is similar. Give a reason for your answer.1. 2.

3. 4.

Similarity of triangles is:

7

1. Reflexive___________________________.2. Symmetric _________________________ .3. Transitive __________________________________________________.

Question: How is proving similar triangles the same or different from proving congruent triangles?

Find Parts of Similar Triangles:Identify the similar triangles in each figure. Explain why they are similar and find the missing measures.Example:a. Find x and y b. Find x and y c. Find x and y

Level 3 HomeworkSimilar Triangles Postulates: SSS, AA, SAS Worksheet

Section 1.3 Level 4 Objectives8

Students will be able to recognize and use proportional relationships of corresponding perimeters of similar triangles.Students will be able to use similar triangles to solve word problems.

Find Parts of Similar Triangles:

Directions: Identify the similar triangles. Find x and the measures of the indicated sides.1. Find x 2. JL and LM

3. 4.

Use the given information to solve the problems.9

Find Parts of Similar Triangles Cont’d:Proportional Perimeters Theorem:If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides.Example: Each pair of triangles is similar. Find the perimeter of the indicated triangle.1.

Directions: Each Pair of triangles is similar. Find the perimeter of the indicated triangle.1. 2.

Indirect Measurement:

10

Examples:

A person 6 ft tall casts a 1.5 ft long shadow at the same time that a flag pole casts a 7 ft long shadow. How tall is the flagpole.Figure and Solution:

You Try:1.

2. A light house casts a 128- foot shadow. A nearby lamppost that measures 5ft 3inches casts an 8ft shadow. What is the height of the lighthouse.

Level 4 Homework

Similar Triangles Worksheet

11