# 7.4.5. Geometric Constructions

What does the following figure illustrate?

• Aa perpendicular to a straight line originating from it
• Ba bisector of an angle
• Ca perpendicular from a point lying outside a straight line
• Da straight line parallel to another line

### Example

What does the following figure illustrate?

• Aa perpendicular to a straight line originating from it
• Ba bisector of an angle
• Ca perpendicular from a point lying outside a straight line
• Da straight line parallel to another line

### Solution

The figure shows the geometric construction resulting from the following steps:

• Start with line , with . Using a compass with as the centre, draw two arcs on different sides of to intersect . Name the intersections and .
• Using and as centres , draw two more arcs to intersect above . Name the intersection of the arcs .
• Draw , which is perpendicular to .

Therefore, the figure shows a ray that is perpendicular to and originating from a straight line.

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