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Bianca Stratford
2/2/2023
Geometry
U4L7 CPCTC and Proofs Review - All Methods Notes
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:
2/2/2023
234
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:
This proof utilizes the definition of a midpoint and vertical angles to establish triangle congruence using the SAS theorem before applying CPCTC.
This proof employs the definition of an angle bisector and the ASA theorem to prove triangle congruence before using CPCTC.
This proof combines alternate interior angles, the definition of a midpoint, and vertical angles to establish triangle congruence using the AAS 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.
10
329
Isosceles & Equilateral Triangles-1
What are the properties of isosceles and equilateral triangles? How can we use these properties to solve missing angle or missing side problems?
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370
Congruent Triangles
What are congruent Triangles? How do we label them, represent them, identify their parts and use their congruent parts for problem solving?
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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:
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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:
This proof utilizes the definition of a midpoint and vertical angles to establish triangle congruence using the SAS theorem before applying CPCTC.
This proof employs the definition of an angle bisector and the ASA theorem to prove triangle congruence before using CPCTC.
This proof combines alternate interior angles, the definition of a midpoint, and vertical angles to establish triangle congruence using the AAS 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.
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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 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:
This proof uses the SSS congruence theorem to establish that triangle ABC is congruent to triangle ADC, then applies CPCTC to prove the congruence of the angles.
This proof employs the AAS 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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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❗️❗️⚠️
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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
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The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
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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
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I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
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
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
Android user
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
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
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
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
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
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
iOS user
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
