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Special Right Triangles

Easy Ways to Find Missing Sides in Special Right Triangles

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Easy Ways to Find Missing Sides in Special Right Triangles
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A comprehensive guide to understanding 45 45 90 triangle theorem and solving 30 60 90 triangle side lengths. This mathematical concept focuses on special right triangles and their unique properties for calculating missing sides.

  • Special right triangles (45-45-90 and 30-60-90) have fixed angle measurements and proportional side lengths
  • The 45-45-90 triangle has congruent legs and a hypotenuse that is √2 times the leg length
  • In a 30-60-90 triangle, the hypotenuse is twice the shorter leg, and the longer leg is √3 times the shorter leg
  • These triangles are fundamental in mathematics and frequently appear in advanced coursework
  • Understanding these relationships allows for quick calculation of missing sides when given just one measurement

6/27/2023

197

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

45-45-90 Triangle Theorem

This page explains the fundamental properties of the 45-45-90 triangle, which is a right triangle with two 45-degree angles.

Highlight: In a 45-45-90 triangle, both legs are equal in length, and the hypotenuse is √2 times the length of a leg.

Example: If a leg is length S, then the other leg is also S, and the hypotenuse is S√2.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

30-60-90 Triangle Theorem

This page details the characteristics of the 30-60-90 triangle and its side length relationships.

Definition: A 30-60-90 triangle is a right triangle with angles of 30, 60, and 90 degrees.

Highlight: The hypotenuse is always twice the length of the shorter leg, while the longer leg is √3 times the shorter leg.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

Important Note on Applications

This page emphasizes the significance of memorizing these special triangles.

Quote: "These two triangles are very important to memorize. We will use them all semester and they are frequently used in other math classes."

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

Examples Introduction

This page serves as a transition to practical applications of the theorems.

Vocabulary: Examples demonstrate how to apply theoretical knowledge to solve real mathematical problems.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

Example 1: 30-60-90 Triangle

This page demonstrates how to find missing sides in special right triangles when given the hypotenuse of a 30-60-90 triangle.

Example: Given a hypotenuse of 4 units, the short side (opposite to 30°) is 2 units, and the long side (opposite to 60°) is 2√3 units.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

Example 2: 45-45-90 Triangle

This page shows how to solve for missing sides in a 45-45-90 triangle when given one leg.

Example: When one leg is 9 units, the other leg is also 9 units, and the hypotenuse is 9√2 units.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

Example 3: Part 1

This page begins a multi-step example solving a 30-60-90 triangle with a known long side of 18 units.

Highlight: The solution process begins by using the relationship s√3 = 18 to find the value of s.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

Example 3: Part 2

This page continues the solution process, focusing on rationalizing denominators.

Example: The short side (x) is calculated to be 6√3 units through rationalization of the denominator.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

Example 3: Part 3

This page concludes the example by finding the hypotenuse.

Highlight: The hypotenuse (y) is calculated as 12√3 units by doubling the short side length.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

View

Special Right Triangles Introduction

This page introduces the concept of special right triangles, which are essential geometric figures with unique properties that make calculating side lengths more efficient.

Definition: Special right triangles are right triangles with specific angle measurements that create consistent relationships between their sides.

Similar Content

Know U7L2 Special Right Triangles Full Solutions thumbnail

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942

U7L2 Special Right Triangles Full Solutions

U7L2 Special Right Triangles Full Solutions

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Subjects

/

Geometry

/

Right Triangles & Trigonometry

/

Special Right Triangles

Easy Ways to Find Missing Sides in Special Right Triangles

user profile picture

C

@cnnotes

·

52 Followers

Follow

A comprehensive guide to understanding 45 45 90 triangle theorem and solving 30 60 90 triangle side lengths. This mathematical concept focuses on special right triangles and their unique properties for calculating missing sides.

  • Special right triangles (45-45-90 and 30-60-90) have fixed angle measurements and proportional side lengths
  • The 45-45-90 triangle has congruent legs and a hypotenuse that is √2 times the leg length
  • In a 30-60-90 triangle, the hypotenuse is twice the shorter leg, and the longer leg is √3 times the shorter leg
  • These triangles are fundamental in mathematics and frequently appear in advanced coursework
  • Understanding these relationships allows for quick calculation of missing sides when given just one measurement

6/27/2023

197

 

9th/10th

 

Geometry

11

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

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Join milions of students

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45-45-90 Triangle Theorem

This page explains the fundamental properties of the 45-45-90 triangle, which is a right triangle with two 45-degree angles.

Highlight: In a 45-45-90 triangle, both legs are equal in length, and the hypotenuse is √2 times the length of a leg.

Example: If a leg is length S, then the other leg is also S, and the hypotenuse is S√2.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

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By signing up you accept Terms of Service and Privacy Policy

30-60-90 Triangle Theorem

This page details the characteristics of the 30-60-90 triangle and its side length relationships.

Definition: A 30-60-90 triangle is a right triangle with angles of 30, 60, and 90 degrees.

Highlight: The hypotenuse is always twice the length of the shorter leg, while the longer leg is √3 times the shorter leg.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

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Access to all documents

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Important Note on Applications

This page emphasizes the significance of memorizing these special triangles.

Quote: "These two triangles are very important to memorize. We will use them all semester and they are frequently used in other math classes."

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

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By signing up you accept Terms of Service and Privacy Policy

Examples Introduction

This page serves as a transition to practical applications of the theorems.

Vocabulary: Examples demonstrate how to apply theoretical knowledge to solve real mathematical problems.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

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Example 1: 30-60-90 Triangle

This page demonstrates how to find missing sides in special right triangles when given the hypotenuse of a 30-60-90 triangle.

Example: Given a hypotenuse of 4 units, the short side (opposite to 30°) is 2 units, and the long side (opposite to 60°) is 2√3 units.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

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Improve your grades

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By signing up you accept Terms of Service and Privacy Policy

Example 2: 45-45-90 Triangle

This page shows how to solve for missing sides in a 45-45-90 triangle when given one leg.

Example: When one leg is 9 units, the other leg is also 9 units, and the hypotenuse is 9√2 units.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

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Example 3: Part 1

This page begins a multi-step example solving a 30-60-90 triangle with a known long side of 18 units.

Highlight: The solution process begins by using the relationship s√3 = 18 to find the value of s.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

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Example 3: Part 2

This page continues the solution process, focusing on rationalizing denominators.

Example: The short side (x) is calculated to be 6√3 units through rationalization of the denominator.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

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Example 3: Part 3

This page concludes the example by finding the hypotenuse.

Highlight: The hypotenuse (y) is calculated as 12√3 units by doubling the short side length.

Special Right Triangles Theorem 2-4-1 (45-45-90 Triangle) In a 45° - 45°-90° triangle, both legs are congruent and the length of the hypoten

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Special Right Triangles Introduction

This page introduces the concept of special right triangles, which are essential geometric figures with unique properties that make calculating side lengths more efficient.

Definition: Special right triangles are right triangles with specific angle measurements that create consistent relationships between their sides.

Similar Content

Geometry - U7L2 Special Right Triangles Full Solutions

U7L2 Special Right Triangles Full Solutions

41

942

0

Know U7L2 Special Right Triangles Full Solutions thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying