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Cavalieri's Principle and Dissection Methods

Learn Triangle Congruence with SSS, SAS, and CPCTC!

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Learn Triangle Congruence with SSS, SAS, and CPCTC!
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Anwita

@anwita_jvda

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Triangle Congruence and Geometric Proofs - A comprehensive guide exploring triangle congruence SSS SAS proofs, congruence theorems, and geometric relationships.

• The guide covers essential triangle congruence postulates including SSS (Side-Side-Side) and SAS (Side-Angle-Side)
• Introduces the CPCTC theorem triangle congruence concept and its applications in geometric proofs
• Features detailed examples of the Hypotenuse leg theorem example and its practical use
• Explores advanced concepts like ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) congruence
• Demonstrates the application of reflexive property and vertical angles in geometric proofs

11/5/2023

56

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

View

Page 2: Practical Proofs Application

This page demonstrates practical applications of triangle congruence proofs using SSS and SAS postulates. Two detailed examples are presented with step-by-step solutions.

Example: First proof shows triangle EFG congruent to triangle GHE using SSS postulate, utilizing given conditions EF ≅ GH and FG ≅ HE, along with the reflexive property for GE.

Highlight: Second proof demonstrates triangle DRA congruent to triangle DRG using SAS postulate, incorporating right angles and the reflexive property.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

View

Page 3: Advanced Proofs and Hypotenuse-Leg Theorem

This page introduces the Hypotenuse-Leg (HL) Congruence Theorem and continues with more complex proof examples.

Definition: The Hypotenuse-Leg Congruence Theorem states that if the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

Example: A proof involving triangles NOT and RSP demonstrates the application of given conditions and theorem principles.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

View

Page 4: ASA and AAS Congruence

This page explores two additional triangle congruence theorems: Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS).

Definition: ASA Congruence states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Definition: AAS Congruence establishes that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

View

Page 5: CPCTC Theorem Application

This page focuses on the CPCTC theorem and its practical application in geometric proofs.

Definition: CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is a theorem stating that when two triangles are proven congruent, all their corresponding parts are also congruent.

Example: A detailed proof showing JK = JL using angle bisector JM and the ASA theorem, followed by CPCTC application.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

View

Page 6: Extended Proofs

This page provides additional practice with extended proofs, incorporating various concepts learned throughout the unit.

Highlight: The proof combines multiple concepts including vertical angles, midpoint properties, and the CPCTC theorem.

Example: A complex proof involving parallel lines, midpoints, and triangle congruence is presented with detailed steps and reasons.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

View

Page 1: Triangle Congruence Fundamentals

This page introduces the fundamental concepts of triangle congruence, focusing on the SSS and SAS postulates. The content establishes the groundwork for understanding how to prove triangles are congruent using different methods.

Definition: Triangle congruence occurs when all six pairs of corresponding parts between two triangles are equal.

Highlight: Two primary postulates involve sides (SSS and SAS), while one theorem specifically applies to right triangles.

Vocabulary: SSS (Side-Side-Side) - A postulate stating that if all three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Example: The reflexive property of congruence is demonstrated when there is a shared side between triangles, and vertical angles are shown to be equal.

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Subjects

/

Geometry

/

2D & 3D Solids

/

Cavalieri's Principle and Dissection Methods

Learn Triangle Congruence with SSS, SAS, and CPCTC!

user profile picture

Anwita

@anwita_jvda

·

1 Follower

Follow

Triangle Congruence and Geometric Proofs - A comprehensive guide exploring triangle congruence SSS SAS proofs, congruence theorems, and geometric relationships.

• The guide covers essential triangle congruence postulates including SSS (Side-Side-Side) and SAS (Side-Angle-Side)
• Introduces the CPCTC theorem triangle congruence concept and its applications in geometric proofs
• Features detailed examples of the Hypotenuse leg theorem example and its practical use
• Explores advanced concepts like ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) congruence
• Demonstrates the application of reflexive property and vertical angles in geometric proofs

11/5/2023

56

 

9th/10th

 

Geometry

4

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

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Page 2: Practical Proofs Application

This page demonstrates practical applications of triangle congruence proofs using SSS and SAS postulates. Two detailed examples are presented with step-by-step solutions.

Example: First proof shows triangle EFG congruent to triangle GHE using SSS postulate, utilizing given conditions EF ≅ GH and FG ≅ HE, along with the reflexive property for GE.

Highlight: Second proof demonstrates triangle DRA congruent to triangle DRG using SAS postulate, incorporating right angles and the reflexive property.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

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

Page 3: Advanced Proofs and Hypotenuse-Leg Theorem

This page introduces the Hypotenuse-Leg (HL) Congruence Theorem and continues with more complex proof examples.

Definition: The Hypotenuse-Leg Congruence Theorem states that if the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

Example: A proof involving triangles NOT and RSP demonstrates the application of given conditions and theorem principles.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

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

Access to all documents

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Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: ASA and AAS Congruence

This page explores two additional triangle congruence theorems: Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS).

Definition: ASA Congruence states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Definition: AAS Congruence establishes that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 5: CPCTC Theorem Application

This page focuses on the CPCTC theorem and its practical application in geometric proofs.

Definition: CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is a theorem stating that when two triangles are proven congruent, all their corresponding parts are also congruent.

Example: A detailed proof showing JK = JL using angle bisector JM and the ASA theorem, followed by CPCTC application.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

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

Page 6: Extended Proofs

This page provides additional practice with extended proofs, incorporating various concepts learned throughout the unit.

Highlight: The proof combines multiple concepts including vertical angles, midpoint properties, and the CPCTC theorem.

Example: A complex proof involving parallel lines, midpoints, and triangle congruence is presented with detailed steps and reasons.

Triangle congruence SSS & SAS Triangle congruence - If all 6 pairs of corresponding 2 postulates involve 2 Sides I theorem & I postulates in

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

Page 1: Triangle Congruence Fundamentals

This page introduces the fundamental concepts of triangle congruence, focusing on the SSS and SAS postulates. The content establishes the groundwork for understanding how to prove triangles are congruent using different methods.

Definition: Triangle congruence occurs when all six pairs of corresponding parts between two triangles are equal.

Highlight: Two primary postulates involve sides (SSS and SAS), while one theorem specifically applies to right triangles.

Vocabulary: SSS (Side-Side-Side) - A postulate stating that if all three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Example: The reflexive property of congruence is demonstrated when there is a shared side between triangles, and vertical angles are shown to be equal.

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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

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