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Name: Period: Date: Topic: Unit 4Proportions and Similarity Packet #1 CCSS Leve l Description 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.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Leve l 1 1. Students will be able to write ratios. 2. Students will be able to set up and solve proportions. CRS Solve word problems containing several rates, proportions, or percentages. Use scale factors to determine the magnitude of a size change. Draw conclusions based on a set of conditions. Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas. Use several angle properties to find an unknown angle measure. Leve l 2 1. Students will be able to identify similar figures. Leve l 3 1. Students will be able to solve problems using scale factors. Leve l 4 1. Students will be able to solve word problems applying properties of proportions. 2. Students will be able to apply proportional parts and scale factors to solve geometric problems. 1

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Name:Period:Date:

Topic: Unit 4Proportions and Similarity Packet #1

CCSS

Level

Description

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

Level 1

1. Students will be able to write ratios.

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

CRS

Solve word problems containing several rates, proportions, or percentages.

Use scale factors to determine the magnitude of a size change.

Draw conclusions based on a set of conditions.

Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas.

Use several angle properties to find an unknown angle measure.

Level 2

1. Students will be able to identify similar figures.

Level 3

1. Students will be able to solve problems using scale factors.

Level 4

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

2. Students will be able to apply proportional parts and scale factors to solve geometric problems.

Level 1

Ratio:

Example(s):

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.

Proportion:

Example(s):

Directions: Solve the following proportions.

1. = x =

2. = y =

3. = x =

4. = x =

5. = 8 a =

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

Practice

Page 284

#1, 3-8, 28-35

Level 2

Similar Polygons:

Symbol:

Example:

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

Similarity statement

Congruent angles

Corresponding sides

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

1.

2.

3.

4.

Practice

Page 293

#4, 5, 6, 7, 11-14

Level 3

Scale Factor:

Example:

In general:

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

1.

2.

3.

4.

5.

PracticePage 292

#1, 15, 21-23, 53-55

Level 4

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 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.

Practice

Page 285

#9, 10, 19-22, 26-27

Page 293

#6, 7, 34-39

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