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Proving Triangle Congruence - SSS and SAS Examples

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Paylee

3/6/2023

Geometry

Triangle Proofs SSS S

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Geometry

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Congruent Triangles

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Triangle Congruence from Transformations

Proving Triangle Congruence - SSS and SAS Examples

Triangle Congruence Proofs guide explains the five fundamental methods for proving triangles congruent: SSS, SAS, ASA, AAS, and HL. This comprehensive resource details how to apply these theorems with practical examples and step-by-step proofs.

• The guide emphasizes the importance of understanding congruent triangles and their properties
• Detailed explanations of SSS congruent triangles and SAS congruent triangles with multiple examples
• Clear distinction between valid congruence proofs and non-valid methods (like AAA)
• Step-by-step breakdown of proof statements and reasons
• Visual demonstrations of each theorem application

...

3/6/2023

774

<h2 id="introduction">Introduction</h2> <p>Triangle proofs SSS, SAS, and other methods can be used to prove triangles congruent. There are f

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SSS Congruence Theorem

The page details the Side-Side-Side (SSS) congruence theorem with practical examples and proofs.

Definition: The SSS congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Example: A detailed proof showing ΔPQR ≅ ΔSTR where:

  • PQ = ST
  • QR = TR
  • R is the midpoint of PS

Highlight: The proof plan must identify all three pairs of congruent sides before concluding triangle congruence.

<h2 id="introduction">Introduction</h2> <p>Triangle proofs SSS, SAS, and other methods can be used to prove triangles congruent. There are f

View

SAS Congruence Theorem

This section covers the Side-Angle-Side (SAS) congruence theorem with detailed examples and applications.

Definition: The SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Example: A proof demonstrating ΔJMN ≅ ΔLNM where:

  • JM = LN
  • ∠JMN = ∠LNM
  • MN is common to both triangles
<h2 id="introduction">Introduction</h2> <p>Triangle proofs SSS, SAS, and other methods can be used to prove triangles congruent. There are f

View

Advanced SAS Applications

The final page presents advanced applications of the SAS congruence theorem with complex examples.

Example: A proof showing ΔABD ≅ ΔCBD using:

  • AB = CB
  • BD bisects ∠ABC
  • BD is common to both triangles

Highlight: The importance of identifying the included angle between congruent sides is emphasized throughout the proofs.

Vocabulary: Angle bisector creates two congruent angles, which is crucial for many SAS proofs.

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Subjects

/

Geometry

/

Congruent Triangles

/

Triangle Congruence from Transformations

Proving Triangle Congruence - SSS and SAS Examples

user profile picture

Paylee

@paylee_zmgg

·

165 Followers

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Triangle Congruence Proofs guide explains the five fundamental methods for proving triangles congruent: SSS, SAS, ASA, AAS, and HL. This comprehensive resource details how to apply these theorems with practical examples and step-by-step proofs.

• The guide emphasizes the importance of understanding congruent triangles and their properties
• Detailed explanations of SSS congruent triangles and SAS congruent triangles with multiple examples
• Clear distinction between valid congruence proofs and non-valid methods (like AAA)
• Step-by-step breakdown of proof statements and reasons
• Visual demonstrations of each theorem application

...

3/6/2023

774

 

Geometry

57

<h2 id="introduction">Introduction</h2> <p>Triangle proofs SSS, SAS, and other methods can be used to prove triangles congruent. There are f

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Access to all documents

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Join milions of students

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SSS Congruence Theorem

The page details the Side-Side-Side (SSS) congruence theorem with practical examples and proofs.

Definition: The SSS congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Example: A detailed proof showing ΔPQR ≅ ΔSTR where:

  • PQ = ST
  • QR = TR
  • R is the midpoint of PS

Highlight: The proof plan must identify all three pairs of congruent sides before concluding triangle congruence.

<h2 id="introduction">Introduction</h2> <p>Triangle proofs SSS, SAS, and other methods can be used to prove triangles congruent. There are f

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

SAS Congruence Theorem

This section covers the Side-Angle-Side (SAS) congruence theorem with detailed examples and applications.

Definition: The SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Example: A proof demonstrating ΔJMN ≅ ΔLNM where:

  • JM = LN
  • ∠JMN = ∠LNM
  • MN is common to both triangles
<h2 id="introduction">Introduction</h2> <p>Triangle proofs SSS, SAS, and other methods can be used to prove triangles congruent. There are f

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

Advanced SAS Applications

The final page presents advanced applications of the SAS congruence theorem with complex examples.

Example: A proof showing ΔABD ≅ ΔCBD using:

  • AB = CB
  • BD bisects ∠ABC
  • BD is common to both triangles

Highlight: The importance of identifying the included angle between congruent sides is emphasized throughout the proofs.

Vocabulary: Angle bisector creates two congruent angles, which is crucial for many SAS proofs.

<h2 id="introduction">Introduction</h2> <p>Triangle proofs SSS, SAS, and other methods can be used to prove triangles congruent. There are f

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

Introduction to Triangle Congruence Proofs

This page introduces the five fundamental ways to prove triangles are congruent. The methods covered include SSS, SAS, ASA, AAS, and HL (Hypotenuse-Leg) theorems.

Definition: CPCTC (Corresponding Parts of Congruent Triangles are Congruent) states that when two triangles are proven congruent, their corresponding parts are also congruent.

Highlight: AAA (three pairs of congruent angles) does NOT prove triangle congruence.

Vocabulary: Included angle refers to the angle formed between two sides of a triangle.

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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

20 M

Students use Knowunity

#1

In Education App Charts in 17 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