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How to Construct Perpendicular and Angle Bisectors Easily

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Safir Yafi Chowdury

18/04/2023

Maths

Constructing Bisector

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Geometry & measures

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Angles

How to Construct Perpendicular and Angle Bisectors Easily

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:

  • Constructing perpendicular bisectors of line segments
  • Creating angle bisectors for various angle measures
  • Drawing perpendicular lines from points on and off given lines
  • Applying these constructions to solve geometric problems

• The guide provides detailed instructions with visual examples for each construction method.
• Practice exercises are included to reinforce understanding of the techniques.
• Important geometric concepts like perpendicular lines, bisectors, and arcs are defined and explained.

...

18/04/2023

705

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

View

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

View

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

View

Construction Practice and Applications

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

Task 1 (15 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

View

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 (90 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

View

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

View

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

View

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

View

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

View

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Subjects

Maths

Geometry & measures

Angles

 

Maths

•

705

•

2 Aug 2025

•

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

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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

Construction Practice and Applications

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

Task 1 (15 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!

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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 (90 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

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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
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
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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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

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