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Dec 8, 2025
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Beginner Geometry Class Notes
A
Alice Lebedev-Migdal
@alicelebedevmigdal_vffh
1 / 5
Basic Terms of Geometry
Geometry begins with undefined terms that serve as building blocks for everything else. A point has no size and is represented by capital letters like A or B. A line has no thickness and can be labeled either with two points (AB) or a lowercase letter.
A plane is a flat surface with no thickness, typically labeled with lowercase letters or Greek letters like α or β. In geometry, we use specific notation to show relationships - for example, "point A belongs to line AB" is written as "A ∈ AB."
All geometric shapes are made up of points, and geometry follows specific axioms. Axiom 1 states every line consists of infinitely many points, while Axiom 2 tells us through any two distinct points, there is exactly one line.
💡 Think of points as tiny dots, lines as strings that go on forever in both directions, and planes as giant sheets of paper that extend infinitely in all directions!
A line segment is a portion of a line with two endpoints, containing all points between them. According to the Length Postulate, we can assign a positive number to every segment representing how many units fit into it.
Measuring Segments
The Parts-Whole Postulate is super useful for finding lengths of line segments. It tells us that the length of a whole segment equals the sum of its parts. For example, if points A, B, C, and D lie on the same line in order, then AD = AB + BC + CD.
This postulate works in both directions. If you need to find a specific part of a segment, you can subtract the other parts from the whole. For instance, AB = AD - .
A midpoint is a special point that divides a segment into two equal parts. If M is the midpoint of segment AB, then AM = MB = ½AB. This relationship is incredibly helpful when solving geometry problems.
🔑 Remember: The Parts-Whole Postulate is like a math equation for segments - the whole equals the sum of its parts!
Applying Segment Concepts
Geometry often involves solving problems about segments and midpoints. When multiple segments have the same midpoint, we can use the properties we've learned to find unknown values.
When working with segment problems, start by writing out what you know. For example, if segment AB is 12 inches and point K divides it so that AK is 5 inches less than KB, you can set up an equation. First, use the Parts-Whole Postulate: AB = AK + KB = 12.
Then, incorporate the relationship between the parts: AK = KB - 5. By substituting and solving these equations, you can find the exact lengths of AK and KB.
🧩 Geometry problems often have multiple steps - break them down into smaller parts and use what you know about segments to solve them!
Rays and Angles
A ray starts at an endpoint and extends infinitely in one direction. When a point divides a line, it creates two rays with a common endpoint. If these rays point in opposite directions, they're called opposite rays.
An angle is formed by two rays with a common endpoint called the vertex. We can label angles in several ways: by their vertex (∠A), by a number (∠1), or by three points with the vertex in the middle (∠AOB).
According to the Angle Measurement Postulate, we can assign a non-negative number to every angle representing its size. The most common unit of measure is degrees. For example, m∠AOB = 48° means the measure of angle AOB is 48 degrees.
📐 Think of an angle like opening scissors - the vertex is the pivot point, and the rays are the blades that can open to different degrees!
Angle Relationships
Angles have special relationships that help us solve geometric problems. Complementary angles add up to 90° - think of them as angles that complete each other to form a right angle.
Supplementary angles add up to 180° - they complete each other to form a straight line. When two angles share a common vertex, a common side, and have no common interior points, they're called adjacent angles.
When two adjacent angles are also supplementary (adding to 180°), they form a linear pair. Linear pairs always lie on a straight line, which is why they equal 180° together.
🔄 Recognizing angle relationships is like having shortcuts in geometry - when you know angles are complementary or supplementary, you can quickly find unknown angle measures!
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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
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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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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
Beginner Geometry Class Notes
A
Alice Lebedev-Migdal
@alicelebedevmigdal_vffh
Geometry is the study of shapes, sizes, and properties of space. It starts with basic building blocks like points, lines, and planes, then builds up to more complex concepts like angles and geometric relationships. Let's explore these fundamental ideas that... Show more
Basic Terms of Geometry
Geometry begins with undefined terms that serve as building blocks for everything else. A point has no size and is represented by capital letters like A or B. A line has no thickness and can be labeled either with two points (AB) or a lowercase letter.
A plane is a flat surface with no thickness, typically labeled with lowercase letters or Greek letters like α or β. In geometry, we use specific notation to show relationships - for example, "point A belongs to line AB" is written as "A ∈ AB."
All geometric shapes are made up of points, and geometry follows specific axioms. Axiom 1 states every line consists of infinitely many points, while Axiom 2 tells us through any two distinct points, there is exactly one line.
💡 Think of points as tiny dots, lines as strings that go on forever in both directions, and planes as giant sheets of paper that extend infinitely in all directions!
A line segment is a portion of a line with two endpoints, containing all points between them. According to the Length Postulate, we can assign a positive number to every segment representing how many units fit into it.
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Measuring Segments
The Parts-Whole Postulate is super useful for finding lengths of line segments. It tells us that the length of a whole segment equals the sum of its parts. For example, if points A, B, C, and D lie on the same line in order, then AD = AB + BC + CD.
This postulate works in both directions. If you need to find a specific part of a segment, you can subtract the other parts from the whole. For instance, AB = AD - .
A midpoint is a special point that divides a segment into two equal parts. If M is the midpoint of segment AB, then AM = MB = ½AB. This relationship is incredibly helpful when solving geometry problems.
🔑 Remember: The Parts-Whole Postulate is like a math equation for segments - the whole equals the sum of its parts!
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Applying Segment Concepts
Geometry often involves solving problems about segments and midpoints. When multiple segments have the same midpoint, we can use the properties we've learned to find unknown values.
When working with segment problems, start by writing out what you know. For example, if segment AB is 12 inches and point K divides it so that AK is 5 inches less than KB, you can set up an equation. First, use the Parts-Whole Postulate: AB = AK + KB = 12.
Then, incorporate the relationship between the parts: AK = KB - 5. By substituting and solving these equations, you can find the exact lengths of AK and KB.
🧩 Geometry problems often have multiple steps - break them down into smaller parts and use what you know about segments to solve them!
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Rays and Angles
A ray starts at an endpoint and extends infinitely in one direction. When a point divides a line, it creates two rays with a common endpoint. If these rays point in opposite directions, they're called opposite rays.
An angle is formed by two rays with a common endpoint called the vertex. We can label angles in several ways: by their vertex (∠A), by a number (∠1), or by three points with the vertex in the middle (∠AOB).
According to the Angle Measurement Postulate, we can assign a non-negative number to every angle representing its size. The most common unit of measure is degrees. For example, m∠AOB = 48° means the measure of angle AOB is 48 degrees.
📐 Think of an angle like opening scissors - the vertex is the pivot point, and the rays are the blades that can open to different degrees!
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Angle Relationships
Angles have special relationships that help us solve geometric problems. Complementary angles add up to 90° - think of them as angles that complete each other to form a right angle.
Supplementary angles add up to 180° - they complete each other to form a straight line. When two angles share a common vertex, a common side, and have no common interior points, they're called adjacent angles.
When two adjacent angles are also supplementary (adding to 180°), they form a linear pair. Linear pairs always lie on a straight line, which is why they equal 180° together.
🔄 Recognizing angle relationships is like having shortcuts in geometry - when you know angles are complementary or supplementary, you can quickly find unknown angle measures!
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?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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4.8/5
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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
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