NAME:
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 6: Defining and Applying Similarity
Lesson 1.6.1: Defining Similarity
Warm-Up 1.6.1
A poster of the tallest buildings in the world hangs in a hallway. The scale on the poster is
0.5 inches = 45 feet.
1. T
he height of the tallest building in the world, Burj Khalifa in Dubai, is about 30.25 inches on
the poster. What is the actual height of Burj Khalifa?
2. T
he height of the tallest building in the United States, Willis Tower (formerly known as Sears
Tower), is about 16 inches on the poster. What is the actual height of Willis Tower?
3. How much taller is Burj Khalifa than Willis Tower?
U1-324
CCGPS Analytic Geometry Teacher Resource
© Walch Education
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 6: Defining and Applying Similarity
Instruction
Lesson 1.6.1: Defining Similarity
Common Core Georgia Performance Standard
MCC9–12.G.SRT.2
Warm-Up 1.6.1 Debrief
A poster of the tallest buildings in the world hangs in a hallway. The scale on the poster is
0.5 inches = 45 feet.
1. T
he height of the tallest building in the world, Burj Khalifa in Dubai, is about 30.25 inches on
the poster. What is the actual height of Burj Khalifa?
Set up a proportion. Let h represent the actual height of the building.
0.5 30.25
=
45
h
0.5h = 45(30.25)
0.5h = 1361.25
Proportion
Simplify through cross-multiplication.
Solve for h.
h = 2722.5
The actual height of Burj Khalifa is approximately 2,722.5 feet.
2. T
he height of the tallest building in the United States, Willis Tower (formerly known as Sears
Tower), is about 16 inches on the poster. What is the actual height of Willis Tower?
Create a proportion to find the actual height of the building, h.
0.5 16
=
45 h
0.5h = 45(16)
0.5h = 720
Proportion
Simplify through cross-multiplication.
Solve for h.
h = 1440
The actual height of Willis Tower is approximately 1,440 feet.
U1-325
© Walch Education
CCGPS Analytic Geometry Teacher Resource
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 6: Defining and Applying Similarity
Instruction
3. How much taller is Burj Khalifa than Willis Tower?
Find the difference of the calculated heights of the two buildings.
2722.5 – 1440 = 1282.5
Burj Khalifa is approximately 1,282.5 feet taller than Willis Tower.
Connection to the Lesson
•
S tudents will use ratios and proportions to determine the ratio of similitude and calculate
missing lengths of similar triangles.
U1-326
CCGPS Analytic Geometry Teacher Resource
© Walch Education