Subjects

Geometry

Congruent Triangles

234

•

Feb 2, 2023

•

2 pages

Easy Congruent Triangles Proofs with CPCTC Answers and Examples

Name: Knowunity
Brand: Knowunity

Bianca Stratford

@biancastratford

Congruent Triangles Proofs with CPCTC: A Comprehensive Guide

This guide... Show more

CONGRUENT TRIANGLE Proofs CPCTC
Stands for Corresponding parts of
congnient triangles are congruent
What is
CPCTC?
Use CPCTC when asked to p

Advanced Applications of CPCTC in Geometric Proofs

This page delves deeper into the application of CPCTC with more complex geometric scenarios, providing CPCTC examples and a CPCTC proofs worksheet with answers.

Three detailed proofs are presented:

Given: X is the midpoint of WY and VZ Prove: ∠XWV ≅ ∠XYZ

This proof utilizes the definition of a midpoint and vertical angles to establish triangle congruence using the SAS $Side-Angle-Side$ theorem before applying CPCTC.

Given: JM bisects ∠KJL, ∠JMK ≅ ∠JML Prove: JK ≅ JL

This proof employs the definition of an angle bisector and the ASA $Angle-Side-Angle$ theorem to prove triangle congruence before using CPCTC.

Given: BC || EF, D is the midpoint of BF Prove: ED ≅ CD

This proof combines alternate interior angles, the definition of a midpoint, and vertical angles to establish triangle congruence using the AAS $Angle-Angle-Side$ theorem before applying CPCTC.

Vocabulary: The reflexive property of congruence states that any geometric object is congruent to itself. This property is often used in these proofs to establish one of the congruent parts needed for triangle congruence theorems.

Highlight: These examples showcase how CPCTC can be applied in various geometric contexts, demonstrating its versatility in proving congruence of corresponding parts after establishing triangle congruence.

These advanced examples reinforce the importance of first proving triangle congruence using established theorems before applying CPCTC to prove the congruence of corresponding parts.

Understanding CPCTC in Congruent Triangle Proofs

CPCTC, which stands for Corresponding Parts of Congruent Triangles are Congruent, is a crucial concept in geometry proofs. This page introduces the concept and provides examples of its application.

Definition: CPCTC $Corresponding Parts of Congruent Triangles are Congruent$ is used to prove that parts of triangles are congruent after establishing that the triangles themselves are congruent.

Highlight: It's important to note that CPCTC can only be used after proving that the triangles are congruent using other methods such as SSS, AAS, or SAS.

The page presents two detailed examples of congruent triangles proofs with CPCTC answers:

Given: AB ≅ AD, BC ≅ DC Prove: ∠BCA ≅ ∠DCA

This proof uses the SSS $Side-Side-Side$ congruence theorem to establish that triangle ABC is congruent to triangle ADC, then applies CPCTC to prove the congruence of the angles.

Given: PS || QR, ∠OPS ≅ ∠SRQ Prove: PQ ≅ RS

This proof employs the AAS $Angle-Angle-Side$ congruence theorem to show that triangle PQS is congruent to triangle RSQ, then uses CPCTC to prove the congruence of the sides.

Example: In the second proof, alternate interior angles and the reflexive property are used to establish the congruence of triangles PQS and RSQ before applying CPCTC.

These examples demonstrate how CPCTC is used in conjunction with other geometric concepts to construct valid proofs.

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Samantha Klich

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Anna

iOS user

Thomas R

iOS user

Brad T

Android user

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

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Aubrey

iOS user

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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Elisha

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Paul T

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Subjects

Geometry

Congruent Triangles

Geometry

•

234

•

Feb 2, 2023

•

2 pages

Easy Congruent Triangles Proofs with CPCTC Answers and Examples

Bianca Stratford

@biancastratford

Congruent Triangles Proofs with CPCTC: A Comprehensive Guide

This guide explores the concept of CPCTC (Corresponding Parts of Congruent Triangles are Congruent) in geometry proofs. It covers:

Definition and application of CPCTC
Step-by-step examples of congruent triangles proofs with CPCTC... Show more

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Advanced Applications of CPCTC in Geometric Proofs

This page delves deeper into the application of CPCTC with more complex geometric scenarios, providing CPCTC examples and a CPCTC proofs worksheet with answers.

Three detailed proofs are presented:

Given: X is the midpoint of WY and VZ Prove: ∠XWV ≅ ∠XYZ

This proof utilizes the definition of a midpoint and vertical angles to establish triangle congruence using the SAS $Side-Angle-Side$ theorem before applying CPCTC.

Given: JM bisects ∠KJL, ∠JMK ≅ ∠JML Prove: JK ≅ JL

This proof employs the definition of an angle bisector and the ASA $Angle-Side-Angle$ theorem to prove triangle congruence before using CPCTC.

Given: BC || EF, D is the midpoint of BF Prove: ED ≅ CD

This proof combines alternate interior angles, the definition of a midpoint, and vertical angles to establish triangle congruence using the AAS $Angle-Angle-Side$ theorem before applying CPCTC.

Vocabulary: The reflexive property of congruence states that any geometric object is congruent to itself. This property is often used in these proofs to establish one of the congruent parts needed for triangle congruence theorems.

Highlight: These examples showcase how CPCTC can be applied in various geometric contexts, demonstrating its versatility in proving congruence of corresponding parts after establishing triangle congruence.

These advanced examples reinforce the importance of first proving triangle congruence using established theorems before applying CPCTC to prove the congruence of corresponding parts.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Understanding CPCTC in Congruent Triangle Proofs

CPCTC, which stands for Corresponding Parts of Congruent Triangles are Congruent, is a crucial concept in geometry proofs. This page introduces the concept and provides examples of its application.

Definition: CPCTC $Corresponding Parts of Congruent Triangles are Congruent$ is used to prove that parts of triangles are congruent after establishing that the triangles themselves are congruent.

Highlight: It's important to note that CPCTC can only be used after proving that the triangles are congruent using other methods such as SSS, AAS, or SAS.

The page presents two detailed examples of congruent triangles proofs with CPCTC answers:

Given: AB ≅ AD, BC ≅ DC Prove: ∠BCA ≅ ∠DCA

This proof uses the SSS $Side-Side-Side$ congruence theorem to establish that triangle ABC is congruent to triangle ADC, then applies CPCTC to prove the congruence of the angles.

Given: PS || QR, ∠OPS ≅ ∠SRQ Prove: PQ ≅ RS

This proof employs the AAS $Angle-Angle-Side$ congruence theorem to show that triangle PQS is congruent to triangle RSQ, then uses CPCTC to prove the congruence of the sides.

Example: In the second proof, alternate interior angles and the reflexive property are used to establish the congruence of triangles PQS and RSQ before applying CPCTC.

These examples demonstrate how CPCTC is used in conjunction with other geometric concepts to construct valid proofs.

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

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

Brad T

Android user

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

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Aubrey

iOS user

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

iOS user

Elisha

iOS user

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

Brad T

Android user

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

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Aubrey

iOS user

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

iOS user

Elisha

iOS user

Paul T

iOS user

Easy Congruent Triangles Proofs with CPCTC Answers and Examples

Advanced Applications of CPCTC in Geometric Proofs

Understanding CPCTC in Congruent Triangle Proofs

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Easy Congruent Triangles Proofs with CPCTC Answers and Examples

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Advanced Applications of CPCTC in Geometric Proofs

Sign up to see the contentIt's free!

Understanding CPCTC in Congruent Triangle Proofs

Similar Content

Isosceles & Equilateral Triangles-1

Congruent Triangles

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

Students love us — and so will you.

4.9/5

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