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Construction of a Perpendicular Bisector

Yesterday's lesson was about constructing a circle using a pair of compasses. Todays lesson continues about construction, but this time, constructing a perpendicular bisector, using a ruler to draw a line segment and a pair of compasses to construct arcs.

Perpendicular bisector:

To bisect a line means to cut the line into two equal parts. The bisector is the thing doing the cutting. When constructing a perpendicular bisector means that the bisector will ALWAYS cross the line segment at a 90 degree angle (Right angle).

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Prior knowledge learners should have:

• Using a ruler and pencil to draw line segments

Using a ruler to draw a line segment

• Constructing arcs

In the introduction part of your lesson, teachers can show the learners drawings of arcs.

Drawing of an arc

Remind your learners that an arc is part of a circle.

As an activity, let learners draw the following:

1. Draw an arc using a radius of 3cm
2. Draw an arc bigger that a quarter circle, using a radius of 5 cm.
3. Draw an arc smaller than a quarter circle, using a radius of 5cm.

Constructing a perpendicular bisector

Activity: 

Constructing line segment CD that is perpendicular to line segment AB using a pair of compasses and a ruler.

Teachers can explain the following steps to the learners:

Step 1:

• Draw line segment AB. (Let learners draw a line of 6cm)

• Open your pair of compasses to more than half of the length of line segment AB. (We can take 4cm)  

Measure 4cm on the ruler

• Place the sharp point of your pair of compasses on point A as shown below:

Step 2:

• Draw an arc as shown below (with a radius of 4cm)

• Without changing the radius, place your pair of compasses on point B and draw an arc that cuts the first arc your drew.

• Mark the points of intersections C and D as shown above.

Step 4:

• Draw a line segment that passes through points C and D

Now learners can see that line segment CD intersects line AB at an angle of 90 degrees. 

Learners can also use this to construct pattern 1 of yesterday's lesson

Teachers can use one of the previous lessons as an example of measuring angles.

Conclusion:

• Teachers must emphasize that this construction must be done accurately
• Constructions must be done neatly.

For homework, teachers can give their learners different lengths of line segments.

Learners have to construct perpendicular bisectors, using their pair of compasses.

Ask your learners where in the class they can see perpendicular lines. 

Ask them what do they think would happen if buildings was not built perpendicularly???

You will be amazed by some of the answers!!