Text of Honors Geometry Unit 5 – Similarity and Dilations Lesson One Proportion and Similarity
Honors Geometry Unit 5 – Similarity and Dilations
Lesson OneProportion and Similarity
• I can define similar figures, proportion, ratio
• I can find a scale factor between similar figures
What is a Ratio?
• We discussed ratios in Unit 1
• To compare two quantities: a and b– We write a : b
– Which implies
• Ratios do not include units of measurement
Ratios• Ratios can also be expressed as decimals
• In this case, the ratio is referred to as a unit ratio
• Ex: Batting Averagehits vs. at bats: 327.0
Write and Simplify Ratios
SCHOOL The total number of students who participate in sports programs at Central High School is 520. The total number of students in the school is 1850. Find the athlete-to-student ratio to the nearest tenth.
To find this ratio, divide the number of athletes by the total number of students.
Answer: The athlete-to-student ratio is 0.3.
0.3 can be written as
• When two ratios are set equal to each other, the equation is called a proportion
• We solve these equations by cross multiplying
Use Cross Products to Solve Proportions
Answer: x = –2
Add 30 to each side.
Divide each side by 24.
A. AB. BC. CD. D
A. n = 9
B. n = 8.9
C. n = 3
D. n = 1.8
Use Proportions to Make Predictions
PETS Monique randomly surveyed 30 students from her class and found that 18 had a dog or a cat for a pet. If there are 870 students in Monique’s school, predict the total number of students with a dog or a cat.
Write and solve a proportion that compares the number of students who have a pet to the number of students in the school.