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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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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

783

<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 SSSSSS 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 SASSAS 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

 

Geometry

•

783

•

Mar 6, 2023

•

4 pages

Proving Triangle Congruence - SSS and SAS Examples

user profile picture

Paylee

@paylee_zmgg

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.

•... Show more

<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 SSSSSS 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.

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SAS Congruence Theorem

This section covers the Side-Angle-Side SASSAS 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

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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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Improve your grades

Join milions of students

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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−LegHypotenuse-Leg theorems.

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

Highlight: AAA threepairsofcongruentanglesthree 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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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Brad T

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

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Android user

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Greenlight Bonnie

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Aubrey

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Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

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THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user