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Diego
10/28/2023
Geometry
Geo & Trig Fundamentals - Study Guide
479
•
Oct 28, 2023
•
Diego
@diegofiz
This comprehensive guide covers essential geometry and trigonometry fundamentals for... Show more
This section focuses on the Pythagorean theorem, its applications, and different types of triangles.
Definition: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides : a² + b² = c².
The guide covers the following subtopics:
Approximating Square Roots: A method to estimate square roots using known perfect squares.
Triangle Classification:
Determining if Three Measures Form a Triangle: The sum of any two sides must be greater than the third side.
Example: To solve a Pythagorean theorem problem when given the lengths of two sides : 3² + 4² = c² 9 + 16 = 25 c = √25 = 5
Highlight: The Pythagorean theorem can also be used to determine if a triangle is right, acute, or obtuse by comparing the sum of the squares of the two shorter sides to the square of the longest side.
This section introduces the distance and midpoint formulas, which are essential for solving problems involving coordinates on a graph.
Definition: The distance formula calculates the length between two points on a coordinate plane, while the midpoint formula finds the coordinates of the point exactly in the middle of two given points.
The guide provides the following formulas:
Example: To find the distance between points (4,2) and (8,4): d = √ d = √ d = √ d = √20 ≈ 4.47
The guide also explains how to find missing endpoints when given one endpoint and the midpoint.
Highlight: Mastering these formulas is crucial for solving more complex geometry problems involving coordinate geometry and analytic geometry.
This final section covers similar triangles and introduces quadratic equations in the context of geometry problems.
Definition: Similar triangles have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are proportional.
The guide explains how to solve problems involving similar triangles using proportions and cross-multiplication. It also introduces the concept of congruent triangles, which are both similar and equal in size.
Example: To solve a similar triangle problem, set up proportions using corresponding sides and cross-multiply: / = (another side of triangle 1) / (corresponding side of triangle 2)
The section concludes with an introduction to quadratic equations in geometry, including:
Highlight: Understanding how to apply quadratic equations to geometry problems is an advanced skill that combines algebraic and geometric reasoning.
This final page summarizes important formulas and concepts covered in the guide, including:
Highlight: Memorizing these key formulas and understanding when to apply them is crucial for success in high school geometry and trigonometry.
The guide emphasizes the importance of practice and provides additional notes and tips for solving various types of geometry problems, from simple proportions to more complex quadratic equations in geometric contexts.
This section introduces various types of angle pairs and their properties, as well as the concept of parallel lines and the angles formed when they are intersected by a transversal.
Definition: Angle pairs are two angles that have a specific relationship to each other based on their position or measure.
The guide covers the following types of angle pairs:
Example: For complementary angles, if one angle is 45°, the other angle must also be 45° since 45° + 45° = 90°.
The guide then introduces parallel lines and the angles formed when they are intersected by a transversal:
Vocabulary: Parallel lines are coplanar lines that never intersect and have the same slope.
When parallel lines are cut by a transversal, the following angle relationships are formed:
Highlight: Understanding these angle relationships is crucial for solving complex geometry problems involving parallel lines and transversals.
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.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
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
Diego
@diegofiz
This comprehensive guide covers essential geometry and trigonometry fundamentals for high school students, focusing on angle pairs, parallel lines, the Pythagorean theorem, distance and midpoint formulas, and similar triangles. It provides clear explanations, examples, and practice problems to help... Show more
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This section focuses on the Pythagorean theorem, its applications, and different types of triangles.
Definition: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides : a² + b² = c².
The guide covers the following subtopics:
Approximating Square Roots: A method to estimate square roots using known perfect squares.
Triangle Classification:
Determining if Three Measures Form a Triangle: The sum of any two sides must be greater than the third side.
Example: To solve a Pythagorean theorem problem when given the lengths of two sides : 3² + 4² = c² 9 + 16 = 25 c = √25 = 5
Highlight: The Pythagorean theorem can also be used to determine if a triangle is right, acute, or obtuse by comparing the sum of the squares of the two shorter sides to the square of the longest side.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This section introduces the distance and midpoint formulas, which are essential for solving problems involving coordinates on a graph.
Definition: The distance formula calculates the length between two points on a coordinate plane, while the midpoint formula finds the coordinates of the point exactly in the middle of two given points.
The guide provides the following formulas:
Example: To find the distance between points (4,2) and (8,4): d = √ d = √ d = √ d = √20 ≈ 4.47
The guide also explains how to find missing endpoints when given one endpoint and the midpoint.
Highlight: Mastering these formulas is crucial for solving more complex geometry problems involving coordinate geometry and analytic geometry.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This final section covers similar triangles and introduces quadratic equations in the context of geometry problems.
Definition: Similar triangles have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are proportional.
The guide explains how to solve problems involving similar triangles using proportions and cross-multiplication. It also introduces the concept of congruent triangles, which are both similar and equal in size.
Example: To solve a similar triangle problem, set up proportions using corresponding sides and cross-multiply: / = (another side of triangle 1) / (corresponding side of triangle 2)
The section concludes with an introduction to quadratic equations in geometry, including:
Highlight: Understanding how to apply quadratic equations to geometry problems is an advanced skill that combines algebraic and geometric reasoning.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This final page summarizes important formulas and concepts covered in the guide, including:
Highlight: Memorizing these key formulas and understanding when to apply them is crucial for success in high school geometry and trigonometry.
The guide emphasizes the importance of practice and provides additional notes and tips for solving various types of geometry problems, from simple proportions to more complex quadratic equations in geometric contexts.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This section introduces various types of angle pairs and their properties, as well as the concept of parallel lines and the angles formed when they are intersected by a transversal.
Definition: Angle pairs are two angles that have a specific relationship to each other based on their position or measure.
The guide covers the following types of angle pairs:
Example: For complementary angles, if one angle is 45°, the other angle must also be 45° since 45° + 45° = 90°.
The guide then introduces parallel lines and the angles formed when they are intersected by a transversal:
Vocabulary: Parallel lines are coplanar lines that never intersect and have the same slope.
When parallel lines are cut by a transversal, the following angle relationships are formed:
Highlight: Understanding these angle relationships is crucial for solving complex geometry problems involving parallel lines and transversals.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
36
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This includes formulas for algebra, analytic geometry, soldi geometry, integral calculus, differential calculus and statistics and probability.
Calculus 1Multiple right triangle word problems and how to solve them.
Algebra 2The unit circle, signs of the trig functions in the four quadrants, and key identities.
Pre-CalculusExplore key trigonometric concepts and problem-solving techniques in right triangles. This resource covers trigonometric ratios (SOH CAH TOA), how to label triangle sides, and step-by-step examples for finding lengths and angles. Ideal for students preparing for exams or needing a refresher on trigonometry fundamentals.
MathsThis involves concepts like trigonometric special angle, angle of elevation and depression, trigonometric functions, trigonometric identities and factor theorem.
TrigonometryApp Store
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
