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Similar Figures

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Similar Figures

Study Guide

Key Definition

Two figures are similar if they have the same shape, their corresponding angles are congruent, and the ratios of the lengths of their corresponding sides are equal.

Important Notes

Similar figures have corresponding angles that are congruent.
The scale factor is the ratio of any two corresponding lengths.
$\sim$ means 'is similar to'.
When $ABC \sim DEF$, $\angle A \cong \angle D$, $\angle B \cong \angle E$, $\angle C \cong \angle F$.
Ratios of corresponding sides are equal: $\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{DF}$.

Mathematical Notation

$\sim$ means 'is similar to'

$\cong$ means 'is congruent to'

$\angle$ denotes an angle

$\frac{a}{b}$ represents a fraction

$\sqrt{x}$ represents a square root

Remember to use proper notation when solving problems

Why It Works

The concept of similarity helps us understand proportional relationships in geometry, allowing us to apply known measurements to unknown ones using scale factors.

Remember

In similar figures, all corresponding angles are equal, and all corresponding side lengths are proportional.

Quick Reference

Corresponding Angles:$\angle A \cong \angle D$

Corresponding Sides:$\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{DF}$

Understanding Similar Figures

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Similar figures have the same shape with proportional sides.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following ratios could represent the scale factor between two congruent figures?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have a photo that you want to enlarge. The original dimensions are 4 inches by 6 inches. If the enlarged photo is 8 inches wide, what will be its height?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Prove that two triangles with two pairs of congruent angles are similar.

Challenge Quiz

Single Choice Quiz

Advanced

Given $\triangle ABC \sim \triangle DEF$, if $AB = 6$, $BC = 8$, and $DE = 9$, find $EF$.

Recap

Watch & Learn

Review key concepts and takeaways