Constructing different angles and shapes

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In this lesson, we will look at constructing different angles and shapes using compasses

• 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.

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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