3.2 Construct different types of triangles  (Page 2/2)

2. Try doing the following:

• Draw any acute-angled $\Delta$ PQR .
• Construct PS $$ QR .
• What is the meaning of PS $$ QR ?

Activity 4

Constructing inscribed and circumscribed circles

[lo 3.4, 3.5, 4.7]

1. Constructing a circumscribed circle:

• Draw any acute-angled triangle.
• Bisect all three angles. You will notice that the tree bisecting lines meet in a single point.
• Try to locate the distance where you could position your compass to draw a circle within or around the triangle.
• Explain what the distance was at which you were able to draw an accurate circle around the triangle.

• What is this distance called?

• What type of circle could you draw?

1.7 Conclusion: A . circle can be constructed by

bisecting the of a triangle.

2. Constructing an inscribed circle:

• Draw any acute-angled triangle.
• Bisect all three angles. You will notice that the tree bisecting lines meet in a single point.
• Try to locate the distance where you could position your compass to draw a circle within or around the triangle.
• Explain what the distance was at which you were able to draw an accurate circle inside the triangle.

• What is this distance called?

• What type of circle could you draw?

2.7 Conclusion: A circle can be constructed by

bisecting the of a triangle.

Activity 5

Constructing a line parallel (ll) to a requested line with the help of a pair of compasses

[lo 3.4, 3.5, 4.7]

1. Required: construct FA ll QR , so that AR = 30 mm.

1.1 Draw an imaginary line (dotted line) FA where the parallel line is required to be.

1.2 Mark A on PR so that AR = 30 mm.

1.3 Position the point of your compasses on R and draw an arc (any size) as indicated.

1.4 Maintaining the setting of your pair of compasses (same size), place the point on A and draw an arc like the previous one.

1.5 Measure the distance, marking it with crosses (x) as indicated.

1.6 Place the compass point on the circle (o) as indicated. This line will intersect the arc and should be on the imaginary line.

1.7 Connect A with the intersecting point of the last drawn line.

1.8 Mark F on PQ. FA will be parallel to QR .

1.9 What does it mean when we say that FA ll QR ?

2. Try doing the following by yourself:

• Construct any obtuse-angled $\Delta$ PQR .
• Bisect PR and designate the centre F .
• Draw a line through F parallel to QR .
• The parallel line PQ must intersect G .

Activity 6

Constructing a parallelogram

[lo 3.4, 3.5, 4.7]

1. You are the owner of a farm in Mpumalanga. You wish to reward one of your farm workers, Michael Mohapi, for his good service of the past 20 years. You present Michael with a stretch of land as a gift. The precondition is that the land must be measured out in the form of a parallelogram according to measurements indicated on a plan.

1.1 The first problem that arises has to do with the fact that Michael does not know what a parallelogram is. Use a sketch to provide Michael with all the characteristics of a parallelogram.

1.2 Also show Michael the mathematical “abbreviation” for a parallelogram, so that he will know what is meant when he sees the relevant "sign".

1.3 Now you have to execute a construction to indicate exactly how the land is to be measured.

Assessment

Memorandum

ACTIVITY 1 – ACTIVITY 5

The memorandum of this learning unit is done by the learners and /or determined by the teacher for corrections.

ACTIVITY 6

1. Both pairs opposite sides are equal.

2. Both pairs opposite sides are parallel.

3. Both pairs opposite angles are equal.

4. Diagonals bisect each other.

5. One pair opposite sides – equal and parallel.