How to Find Similarity and Ratios? (+FREE Worksheet!)

How to Find Similarity and Ratios? (+FREE Worksheet!)

Two figures are similar if they have the same shape. Learn how to use ratios and proportions to solve similarity problems in a few simple steps.

Related Topics

Step by step guide to solve similarity and ratios problems

  • Two or more figures are similar if the corresponding angles are equal, and the corresponding sides are in proportion.
  • To solve the similarity problem, you usually need to create a proportion and solve for the unknown side.

Similarity and Ratios – Example 1:

A girl \(180\) cm tall, stands \(340\) cm from a lamp post at night. Her shadow from the light is \(90\) cm long. How high is the lamp post?

Solution:

Write the proportion and solve for the missing side.
\(\frac{Smaller \ triangle \ height}{Smaller \ triangle \ base} = \frac{Bigger \ triangle \ height}{Bigger \ triangle \ base}\)
\(⇒ \frac{180 \ cm}{90 \ cm }= \frac{x} {90 \ + \ 340 \ cm} ⇒=180 \ × \ 430= 90 × \ x ⇒ 77400= 90 \ x ⇒  x=\frac{77400}{90}=860\) \(cm\)

Similarity and Ratios – Example 2:

A tree \(20\) feet tall casts a shadow \(14\) feet long. Jack is \(10\) feet tall. How long is Jack’s shadow?

Solution:

Write a proportion and solve for the missing number.
\(\frac{20}{14}=\frac{10}{x} → 20 × \ x=10 \ × \ 14\)
\(20 \ x=140→x=\frac{140}{20}=7\)

Similarity and Ratios – Example 3:

A tree\(160\) cm tall, stands \(360\) cm from a lamp post at night. Its shadow from the light is \(90\) cm long. How high is the lamp post?

Solution:

Write the proportion and solve for the missing side.
\(\frac{Smaller \ triangle \ height}{Smaller \ triangle \ base}= \frac{Bigger \ triangle \ height}{Bigger \ triangle \ base}\)
\( ⇒ \frac{160 \ cm}{90 \ cm }= \frac{x} {90+360 \ cm} ⇒160×450= 90 × x ⇒ 72000= 90 \ x ⇒ x=\frac{72000}{90}=800\) \(cm\)

Similarity and Ratios – Example 4:

A tree \(32\) feet tall casts a shadow \(12\) feet long. Jack is \(6\) feet tall. How long is Jack’s shadow?

Solution:

Write a proportion and solve for the missing number.
\( \frac{32}{12}=\frac{6}{x} → 32 × x=6×12\)
\(32x=72→x=\frac{72}{32}=2.25\)

Exercises for Finding Similarity and Ratios

Each pair of figures is similar. Find the missing side.

Download Similarity and Ratios Worksheet

This image has an empty alt attribute; its file name is answer-3.png

Answers

  1. \(\color{blue}{12}\)
  2. \(\color{blue}{2}\)
  3. \(\color{blue}{5}\)
  4. \(\color{blue}{15}\)

Related to "How to Find Similarity and Ratios? (+FREE Worksheet!)"

Top 5 GED Math Study Guides
Top 5 GED Math Study Guides
A Comprehensive Collection of FREE PSAT Math Practice Tests
A Comprehensive Collection of FREE PSAT Math Practice Tests
What’s A Good ACT Score?
What’s A Good ACT Score?
TASC Testing Accommodation and Support for Disabilities
TASC Testing Accommodation and Support for Disabilities
The History of Math Development in the USA
The History of Math Development in the USA
Use of Technology in Math Class That Works
Use of Technology in Math Class That Works
Improving Your Math in College: What You Should Do
Improving Your Math in College: What You Should Do
Top Proven Strategies To Increase Your SAT Math Score
Top Proven Strategies To Increase Your SAT Math Score
Top Math YouTube Channels For High School Students
Top Math YouTube Channels For High School Students
What Kind of Math is on the GRE?
What Kind of Math is on the GRE?

Leave a Reply

30% OFF

SAVE $9.34

Cyber Monday DEAL!

It was $16.99 now it is $7.65

X
55% OFF!

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…