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702

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18 Apr 2023

•

23 pages

How to Construct Perpendicular and Angle Bisectors Easily

user profile picture

Safir Yafi Chowdury

@safirchowdury_positiveskills

How to construct perpendicular and angle bisectorsis a fundamental... Show more

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

Constructing Perpendicular and Angle Bisectors

This page provides detailed instructions for constructing perpendicular and angle bisectors using a compass and ruler.

To construct the perpendicular bisector of a line AB:

  1. Place compass at A, set over halfway and draw two arcs
  2. Repeat from B with the same compass width
  3. Draw the perpendicular bisector through the arc intersection points

To construct the angle bisector of angle BAC:

  1. Place compass at A and draw an arc crossing AB and AC
  2. From the intersections, draw two arcs that intersect
  3. Draw the angle bisector from A through the new intersection point

Example: These techniques can be applied to bisect angles of various measures, such as 60°, 90°, or 110°.

The page also covers how to construct a perpendicular from a point not on the line:

  1. Draw an arc from the point P intersecting the line at two points
  2. Use these intersection points as centers to draw intersecting arcs below the line
  3. Connect P to the new intersection point to create the perpendicular line
DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

Perpendicular Line Construction

This section focuses on constructing a perpendicular line through a specific point on a given line.

Steps to draw a perpendicular to a point P on line AB:

  1. Place compass at P and draw an arc intersecting AB at another point C
  2. With compass at A, draw an arc above AB
  3. Repeat from C with the same compass width
  4. Draw a line from P through the intersection of the upper arcs

Highlight: This method ensures the constructed line is exactly perpendicular to the original line at the chosen point.

The lesson includes practice problems for students to apply these construction techniques:

  1. Construct the perpendicular bisector of a given line segment
  2. Construct the angle bisector of a given angle
  3. Construct the perpendicular bisector of a line segment labeled CD

Example: These problems provide opportunities to practice precise compass and ruler use while reinforcing the concepts of perpendicular and angle bisectors.

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

Construction Practice and Applications

This section provides a set of practice exercises for students to apply their newly learned construction skills.

Task 1 15minutes15 minutes:

  1. Draw an 8cm line and construct its perpendicular bisector
  2. Draw a 6cm line and construct its perpendicular bisector
  3. Draw and construct angle bisectors for the following angles: a) 60° b) 40° c) 90° d) 110° e) 150° f) 54° g) 220°

Highlight: These exercises cover a range of angle measures, helping students become proficient in constructing angle bisectors using a compass for various scenarios.

The remaining pages of the document provide space for students to complete these construction exercises, emphasizing the importance of showing all construction arcs and lines clearly.

Example: When bisecting a 90° angle, students should draw the initial angle, then use their compass to create intersecting arcs that determine the bisector line.

By practicing these constructions, students develop a strong foundation in geometric reasoning and precise drawing techniques essential for more advanced geometry topics.

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

Constructions 1: Perpendicular and Angle Bisectors

This lesson introduces fundamental geometric construction techniques using a compass and ruler. Students will learn how to construct perpendicular bisectors of lines and angle bisectors.

Definition: A perpendicular bisector cuts a line in half at right angles.

The lesson begins with a review of key terms:

Vocabulary:

  • Perpendicular: Lines that intersect at a right 90degree90 degree angle
  • Intersect: To cross over or have a common point
  • Arc: Any smooth curve joining two points

A step-by-step worked example demonstrates how to construct a perpendicular bisector of a line:

  1. Draw a line of given length
  2. Open compass to more than half the line's length
  3. Draw arcs from each endpoint
  4. Connect intersection points of arcs

Highlight: Construction marks should not be erased, as they are part of the solution.

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76
DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76
DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76
DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76
DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76
DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76


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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

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

•

702

•

18 Apr 2023

•

23 pages

How to Construct Perpendicular and Angle Bisectors Easily

user profile picture

Safir Yafi Chowdury

@safirchowdury_positiveskills

How to construct perpendicular and angle bisectors is a fundamental skill in geometry. This guide covers the step-by-step process of constructing perpendicular bisectors of lines and triangles, as well as angle bisectors, using a compass and ruler. Key techniques include:... Show more

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

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Constructing Perpendicular and Angle Bisectors

This page provides detailed instructions for constructing perpendicular and angle bisectors using a compass and ruler.

To construct the perpendicular bisector of a line AB:

  1. Place compass at A, set over halfway and draw two arcs
  2. Repeat from B with the same compass width
  3. Draw the perpendicular bisector through the arc intersection points

To construct the angle bisector of angle BAC:

  1. Place compass at A and draw an arc crossing AB and AC
  2. From the intersections, draw two arcs that intersect
  3. Draw the angle bisector from A through the new intersection point

Example: These techniques can be applied to bisect angles of various measures, such as 60°, 90°, or 110°.

The page also covers how to construct a perpendicular from a point not on the line:

  1. Draw an arc from the point P intersecting the line at two points
  2. Use these intersection points as centers to draw intersecting arcs below the line
  3. Connect P to the new intersection point to create the perpendicular line
DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

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Perpendicular Line Construction

This section focuses on constructing a perpendicular line through a specific point on a given line.

Steps to draw a perpendicular to a point P on line AB:

  1. Place compass at P and draw an arc intersecting AB at another point C
  2. With compass at A, draw an arc above AB
  3. Repeat from C with the same compass width
  4. Draw a line from P through the intersection of the upper arcs

Highlight: This method ensures the constructed line is exactly perpendicular to the original line at the chosen point.

The lesson includes practice problems for students to apply these construction techniques:

  1. Construct the perpendicular bisector of a given line segment
  2. Construct the angle bisector of a given angle
  3. Construct the perpendicular bisector of a line segment labeled CD

Example: These problems provide opportunities to practice precise compass and ruler use while reinforcing the concepts of perpendicular and angle bisectors.

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

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

Construction Practice and Applications

This section provides a set of practice exercises for students to apply their newly learned construction skills.

Task 1 15minutes15 minutes:

  1. Draw an 8cm line and construct its perpendicular bisector
  2. Draw a 6cm line and construct its perpendicular bisector
  3. Draw and construct angle bisectors for the following angles: a) 60° b) 40° c) 90° d) 110° e) 150° f) 54° g) 220°

Highlight: These exercises cover a range of angle measures, helping students become proficient in constructing angle bisectors using a compass for various scenarios.

The remaining pages of the document provide space for students to complete these construction exercises, emphasizing the importance of showing all construction arcs and lines clearly.

Example: When bisecting a 90° angle, students should draw the initial angle, then use their compass to create intersecting arcs that determine the bisector line.

By practicing these constructions, students develop a strong foundation in geometric reasoning and precise drawing techniques essential for more advanced geometry topics.

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

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

Constructions 1: Perpendicular and Angle Bisectors

This lesson introduces fundamental geometric construction techniques using a compass and ruler. Students will learn how to construct perpendicular bisectors of lines and angle bisectors.

Definition: A perpendicular bisector cuts a line in half at right angles.

The lesson begins with a review of key terms:

Vocabulary:

  • Perpendicular: Lines that intersect at a right 90degree90 degree angle
  • Intersect: To cross over or have a common point
  • Arc: Any smooth curve joining two points

A step-by-step worked example demonstrates how to construct a perpendicular bisector of a line:

  1. Draw a line of given length
  2. Open compass to more than half the line's length
  3. Draw arcs from each endpoint
  4. Connect intersection points of arcs

Highlight: Construction marks should not be erased, as they are part of the solution.

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

Sign up to see the contentIt's free!

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By signing up you accept Terms of Service and Privacy Policy

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

Sign up to see the contentIt's free!

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DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

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DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

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DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

Sign up to see the contentIt's free!

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By signing up you accept Terms of Service and Privacy Policy

DO NOW: 5 minutes Estimate 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Work out 546-109.5 448 3 × ²/1/2 X 4 Work out £86.94 6 Expand 12(x + 3) Express 76

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

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

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