Triangle congruence by SSS and SASpostulates is a fundamental... Show more
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Triangle Congruencee by SSS and SAS
523
•
Jul 1, 2025
•
Fun with Triangle Congruence: SSS, SAS, and ASA Explained!
Practice and SAS Postulate
This page provides a practice problem for the SSS postulate and introduces the Side-Angle-Side Postulate.
The practice problem reinforces the application of the SSS postulate:
Example: Given: EG = GH, EF = HF, and F is the midpoint of GI. Prove: Triangle EFG is congruent to Triangle HFG.
The solution demonstrates how to use given information and the definition of a midpoint to prove triangle congruence using the SSS postulate.
The page then introduces the SAS postulate:
Definition: The SAS postulate 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 two triangles are congruent.
This definition is crucial for understanding another method of proving triangle congruence, expanding students' toolkit for geometric proofs.
Highlight: The SAS postulate requires that the angle be included between the two congruent sides, which is a key distinction from the SSS postulate.
Applying SAS Postulate
This page focuses on applying the Side-Angle-Side Postulate through various examples and practice problems. It emphasizes the importance of identifying the correct information needed to prove triangle congruence using SAS.
The first example asks what additional information is needed to prove triangle DEF congruent to triangle DGF using SAS:
Example: Given: EF = GD and DF = FD . The solution explains that the angle EFD or DFG is needed, as it's the angle between the two known congruent sides.
Another example explores what's needed to prove triangle LBE congruent to triangle BNL using SAS:
Example: Given: Angle ELB = Angle BNL and LB = BL . The solution indicates that LE = NL is the additional information needed.
These examples help students understand the specific requirements of the SAS postulate and how to identify missing information in congruence proofs.
Highlight: When using the SAS postulate, it's crucial to ensure that the known angle is included between the two congruent sides.
The page also includes practice problems that ask students to determine whether SSS or SAS can be used to prove triangle congruence, or if there's not enough information provided.
Identifying Congruent Triangles
This final page focuses on identifying when to use the SSS or SAS postulates to prove triangle congruence. It presents several scenarios and asks students to determine which postulate, if any, can be used to prove congruence.
Example: One problem shows two triangles with three pairs of congruent sides marked. The solution explains that SSS can be used to prove these triangles congruent.
Example: Another problem presents two triangles with two congruent sides and one congruent angle marked. The solution points out that SAS cannot be used because the given angle is not included between the congruent sides.
These examples help students distinguish between situations where SSS, SAS, or neither postulate can be applied.
Highlight: It's important to carefully examine the given information and the position of congruent parts when deciding which postulate to use.
The page concludes with a "Got It!" section, reinforcing the concepts learned throughout the lesson.
Vocabulary: Reflexive property is often used in these proofs, stating that a side is congruent to itself.
This comprehensive review of SSS and SAS postulates provides students with the tools to prove triangle congruence in various scenarios, enhancing their understanding of geometric proofs.
Triangle Congruence by SSS & SAS
This page introduces the Side-Side-Side Postulate for proving triangle congruence. The SSS postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Definition: The SSS postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
An example is provided to demonstrate how to use the SSS postulate to prove triangle congruence:
Example: Given: LM = NP, LP = NM, and LN is congruent to itself . Prove: Triangle LMN is congruent to Triangle NPL.
The page also includes a "Got It?" section with another example:
Example: Given: BC = BF, CD = FD, and BD is congruent to itself . Prove: Triangle ABC is congruent to Triangle BFD.
These examples help students understand how to apply the SSS postulate in different scenarios, reinforcing the concept of proving triangles congruent using SSS.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
You have the choice, we offer a 100% secure payment via PayPal or an Amazon gift card. There is no limit to how much you can earn.
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
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
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
Fun with Triangle Congruence: SSS, SAS, and ASA Explained!
Triangle congruence by SSS and SAS postulates is a fundamental concept in geometry. This lesson covers the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates for proving triangle congruence, providing definitions, examples, and practice problems.
Key points:
- SSS postulate: Triangles are... Show more
Practice and SAS Postulate
This page provides a practice problem for the SSS postulate and introduces the Side-Angle-Side Postulate.
The practice problem reinforces the application of the SSS postulate:
Example: Given: EG = GH, EF = HF, and F is the midpoint of GI. Prove: Triangle EFG is congruent to Triangle HFG.
The solution demonstrates how to use given information and the definition of a midpoint to prove triangle congruence using the SSS postulate.
The page then introduces the SAS postulate:
Definition: The SAS postulate 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 two triangles are congruent.
This definition is crucial for understanding another method of proving triangle congruence, expanding students' toolkit for geometric proofs.
Highlight: The SAS postulate requires that the angle be included between the two congruent sides, which is a key distinction from the SSS postulate.
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Improve your grades
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By signing up you accept Terms of Service and Privacy Policy
Applying SAS Postulate
This page focuses on applying the Side-Angle-Side Postulate through various examples and practice problems. It emphasizes the importance of identifying the correct information needed to prove triangle congruence using SAS.
The first example asks what additional information is needed to prove triangle DEF congruent to triangle DGF using SAS:
Example: Given: EF = GD and DF = FD . The solution explains that the angle EFD or DFG is needed, as it's the angle between the two known congruent sides.
Another example explores what's needed to prove triangle LBE congruent to triangle BNL using SAS:
Example: Given: Angle ELB = Angle BNL and LB = BL . The solution indicates that LE = NL is the additional information needed.
These examples help students understand the specific requirements of the SAS postulate and how to identify missing information in congruence proofs.
Highlight: When using the SAS postulate, it's crucial to ensure that the known angle is included between the two congruent sides.
The page also includes practice problems that ask students to determine whether SSS or SAS can be used to prove triangle congruence, or if there's not enough information provided.
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
Identifying Congruent Triangles
This final page focuses on identifying when to use the SSS or SAS postulates to prove triangle congruence. It presents several scenarios and asks students to determine which postulate, if any, can be used to prove congruence.
Example: One problem shows two triangles with three pairs of congruent sides marked. The solution explains that SSS can be used to prove these triangles congruent.
Example: Another problem presents two triangles with two congruent sides and one congruent angle marked. The solution points out that SAS cannot be used because the given angle is not included between the congruent sides.
These examples help students distinguish between situations where SSS, SAS, or neither postulate can be applied.
Highlight: It's important to carefully examine the given information and the position of congruent parts when deciding which postulate to use.
The page concludes with a "Got It!" section, reinforcing the concepts learned throughout the lesson.
Vocabulary: Reflexive property is often used in these proofs, stating that a side is congruent to itself.
This comprehensive review of SSS and SAS postulates provides students with the tools to prove triangle congruence in various scenarios, enhancing their understanding of geometric proofs.
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
Triangle Congruence by SSS & SAS
This page introduces the Side-Side-Side Postulate for proving triangle congruence. The SSS postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Definition: The SSS postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
An example is provided to demonstrate how to use the SSS postulate to prove triangle congruence:
Example: Given: LM = NP, LP = NM, and LN is congruent to itself . Prove: Triangle LMN is congruent to Triangle NPL.
The page also includes a "Got It?" section with another example:
Example: Given: BC = BF, CD = FD, and BD is congruent to itself . Prove: Triangle ABC is congruent to Triangle BFD.
These examples help students understand how to apply the SSS postulate in different scenarios, reinforcing the concept of proving triangles congruent using SSS.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
You have the choice, we offer a 100% secure payment via PayPal or an Amazon gift card. There is no limit to how much you can earn.
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
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
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