Constructing different angles and shapes


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In this lesson, we will look at constructing different angles and shapes using a compass and a straight edge.

  • A 90° angle can be obtained by constructing a perpendicular bisector.
  • A 45° angle can be obtained by bisecting a 90° angle.
  • A 22.5° angle can be obtained by bisecting a 45° angle.
  • A 60° angle can be obtained by constructing an equilateral triangle.
  • A 30° angle can be obtained by bisecting a 60° angle.
  • A 15° angle can be obtained by bisecting a 30° angle.

Example: The figure shows a point A on a straight line. Construct an angle of 45° at point A.


 

Solution: Construct a 90° angle, and then construct an angle bisector to obtain a 45° angle.

bisect 90° to 45°
 

The following video shows

  • how to bisect a line
  • how to bisect an angle
  • how to construct a right angle
  • how to construct a 60° angle
  • how to construct a hexagon



The following video shows

  • how to construct a 120° angle
  • how to construct a 45° angle
  • how to construct a 30° angle
  • how to construct an equilateral triangle
  • how to construct triangle given 3 sides using compasses


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