Let’s learn to construct geometric figures using a ruler and compass. Shapes, angles and lines must be drawn accurately. A ruler is used for a straightedge or drawing straight lines. A compass is used to draw a circle. When making constructions measuring devices are not necessarily used to measure distances because they’re used to make more precise shapes, angles and lines. For instance, any regular polygon is easier to make using a compass and ruler than to draw angles and measure each side using a protractor.
Two lines are perpendicular if the two lines intersect and form a right angle. A perpendicular bisector is if the segment is at its midpoint and it cuts the line, ray or segment into an equal measure.
To construct a perpendicular bisector:
a. Draw point A and a circle with point A as the centre.
b. Draw point B and a circle with point B as the centre.
c. Draw a line connecting point A and B.
d. At the point of intersection of the two circles, draw a line. This is the perpendicular bisector of point A and B.
An angle bisector divides an angle into two equal angles. If the angle bisects, it will make two congruent angles.
To construct an angle bisector:
a. Draw an angle.
b. From the vertex of the angle, draw a circle, as the point of the vertex is the centre.
c. From the two points that the circle cross both sides of the angle, draw two more circles. Where the two circles intersect, draw a line at the point of intersection.
An equilateral triangle is known for its congruent sides and angles. All sides and angles of an equilateral triangle have equal measure.
To construct an equilateral triangle:
a. Draw a line segment.
b. In two endpoints, stretch the compass.
c. Mark on each vertex and draw a line to the point of intersection.
Regular Polygon: Hexagon
A regular hexagon is a figure with all six sides and angles having equal measure.
To construct a regular hexagon:
a. Draw a circle.
b. The radius of the circle is the edge length of the hexagon.
c. Using a compass, stretch it to the size of a radius.
d. Mark the circumference of the circle using the compass.
e. Draw a line that connects the points of intersection or the corners of the hexagon.