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## High school geometry

### Unit 4: Lesson 1

Definitions of similarity

Practicing identifying proportional relationships and solving equations with proportions helps us get ready to learn about similarity.
Let’s refresh some concepts that will come in handy as you start the similarity unit of the high school geometry course. You’ll see a summary of each concept, along with a sample item, links for more practice, and some info about why you will need the concept for the unit ahead.
This article only includes concepts from earlier courses. There are also concepts within this high school geometry course that are important to understanding similarity. If you have not yet mastered the Congruent triangles lesson or the Dilations preserved properties lesson, it may be helpful for you to review those before going farther into the unit ahead.

## Identifying proportional relationships

### What is this, and why do we need it?

A relationship between two quantities is proportional if the ratio between those quantities is always equivalent. We will look at side length ratios to find out whether triangles are similar or not.

### Practice

Problem 1
Triangle A has a height of 2, point, 5, start text, space, c, m, end text and a base of 1, point, 6, start text, space, c, m, end text. The height and base of triangle B are proportional to the height and base of triangle A.
Which of the following could be the height and base of triangle B?

For more practice, go to Proportional relationships.

### Where will we use this?

Here are a few of the exercises where reviewing proportional relationships might be helpful:

## Solve equations with proportions

### What is this, and why do we need it?

When two ratios are equal, we create a proportion equation. If we multiply the equation by both denominators, we can solve the resulting equation just like a linear (or quadratic, but not in this unit) equation. We will set up equations with proportions to find lengths in similar figures.

### Practice

Problem 2.1
Solve for m.
start fraction, 8, divided by, 10, end fraction, equals, start fraction, 6, divided by, m, end fraction
m, equals

For more practice, go to Solving proportions 2.

### Where will we use this?

Here are a few exercises where reviewing proportions equations might be helpful.

## Want to join the conversation?

• i do not understand why he give me a question about:q/q+5=12/27.and suddenly next stop just became:27q=12q+60.what the hell is that number 60 coming form?
(⊙⊙?)