Subjects

Maths

Geometry & measures

Angles

575

•

5 Sept 2023

•

6 pages

Easy Trigonometry and Angles Tips - GCSE Help: Memorize Trigonometry, Parallel Lines, and Polygons

🫶🏼

@aaliyahtasmin

A comprehensive guide to geometry concepts including angles in parallel... Show more

Page 2: Interior and Exterior Angles of Polygons

This page delves deeper into the properties of interior and exterior angles in polygons, with a focus on triangles.

Definition: Interior angle - an angle on the inside of a polygon.

Key points covered:

The sum of interior angles in a triangle is always 180°.

Properties of isosceles triangles: Two sides and two base angles are equal.

Exterior angles of polygons: The sum of exterior angles in any polygon is always 360°.

Example: In a triangle with angles 58°, 80°, and x°, we can find x by solving 58° + 80° + x° = 180°.

The page includes practice problems for calculating unknown angles in various polygons.

Highlight: To find an exterior angle of a regular polygon, use the formula: 360° ÷ number of sides.

Page 3: Advanced Polygon Angle Calculations

This page focuses on more complex angle calculations in regular and irregular polygons.

Practice problems include:

Calculating interior angles of regular polygons with 16, 19, and 18 sides.

Finding missing angles in irregular polygons.

Determining the number of sides in polygons given the sum of interior angles.

Example: For a regular polygon with 16 sides, the size of one interior angle is $16-2$ × 180° ÷ 16 = 157.5°.

The page also covers exterior angles in polygons:

The sum of exterior angles is always 360°.

To find one exterior angle: 360° ÷ number of sides.

Highlight: In a regular polygon, the sum of one interior and one exterior angle is always 180°.

Page 4: Pythagorean Theorem and Its Applications

This page introduces the Pythagorean theorem and its practical applications in geometry.

Definition: Pythagorean theorem - In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides $c² = a² + b²$ .

Key concepts covered:

Using the Pythagorean theorem to find missing sides in right-angled triangles.

Verifying if a triangle is right-angled using the theorem.

Solving real-world problems using the Pythagorean theorem.

Example: In a right-angled triangle with sides 3cm and 4cm, the hypotenuse is √ $3² + 4²$ = 5cm.

The page includes various practice problems and real-world applications, such as calculating distances in navigation.

Highlight: The Pythagorean theorem is a fundamental concept in trigonometry and has numerous practical applications in fields like construction, navigation, and physics.

This comprehensive guide provides students with a solid foundation in trigonometry and angle properties, essential for success in GCSE mathematics. By mastering these concepts and practicing with the provided examples and problems, students will be well-prepared for their exams and future mathematical studies.

Page 4: Pythagoras Theorem

This section introduces the Pythagorean theorem and its applications.

Definition: In a right-angled triangle, c² = a² + b², where c is the hypotenuse.

Example: For a triangle with sides 3cm and 4cm, the hypotenuse is √ $3² + 4²$ = 5cm.

Highlight: The theorem can be used to verify if a triangle is right-angled.

Page 5: Trigonometry Introduction

This page covers basic trigonometric ratios and their applications.

Definition: SOH CAH TOA represents the three main trigonometric ratios: Sine, Cosine, and Tangent.

Vocabulary: Adjacent - the side next to the angle in question $excluding the hypotenuse$ .

Example: sin⁻¹, cos⁻¹, and tan⁻¹ are inverse trigonometric functions used to find angles.

Page 1: Angle Properties and Parallel Lines

This page introduces fundamental angle properties and their applications in parallel lines.

Vocabulary: Corresponding angles, alternate angles, co-interior angles, vertically opposite angles

The page covers the following key concepts:

Angles on parallel lines: Corresponding and alternate angles are equal, while co-interior angles sum to 180°.

Vertically opposite angles are equal.

Properties of parallelogram angles: Opposite angles are equal, and adjacent angles sum to 180°.

Example: In a parallelogram, if one angle is 70°, the adjacent angle is 110° $180° - 70°$ .

The page also introduces the concept of interior angles in polygons:

The sum of interior angles formula: $n-2$ × 180°, where n is the number of sides.

Examples are provided for different polygons $n = 4, 6, 20$ .

Highlight: For a hexagon $n = 6$ , the sum of interior angles is $6-2$ × 180° = 720°.

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Stefan S
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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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Best app on earth! no words because it’s too good
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Basil
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This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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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!
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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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very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
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I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user

Subjects

Maths

Geometry & measures

Angles

Maths
•
575
•
5 Sept 2023
•
6 pages

Easy Trigonometry and Angles Tips - GCSE Help: Memorize Trigonometry, Parallel Lines, and Polygons

🫶🏼

@aaliyahtasmin

A comprehensive guide to geometry concepts including angles in parallel lines, polygons, and trigonometry. This material covers essential GCSE mathematics topics with detailed explanations and practical examples.

Explores fundamental angle relationships in parallel lines including corresponding, alternate, and co-interior... Show more

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

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

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

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

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

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user