3.2 Construct different types of triangles

Mathematics

Grade 8

Ratio and proportion

Measurement

Constructions

Module 17

Constructing different angles and triangles

Activity 1

Constructing different angles and triangles

[lo 3.4, 3.5, 4.7]

1. Drawing an angle:Requirements: pencil, ruler, protractor.

1.1 Always begin by drawing a base line.

1.2 Make a mark, e.g. on the left, and position the protractor on the mark.

1.3 Read your protractor from 0°.

1.4 In the case of an angle that is larger than 180°, the relevant angle size must be deducted from 360° before it is drawn. The angle around the outside (the reflex angle) is the angle that you will have to draw.

E.g. 320°: (360° – 320° = 40°). Draw a 40°angle. The reflex angle now represents the 320°.

2. Construct the following angles and name each one:

• A $\hat{B}$ C = 75°

Type of angle:

2.2 C $\hat{D}$ E = 135°

Type of angle:

2.3 F $\hat{G}$ H = 215°

Type of angle:

3. Constructing a triangle:

Requirements: pencil, ruler, protractor and pair of compasses.

• Always begin by making a rough sketch.
• Then use one of the sides of which the length is provided as a base.
• E.g. construct $\Delta$ ABC with BC = 40 mm, $\hat{B}$ = 70° and $\hat{C}$ = 50°.

Rough sketch:

• To measure a lateral length accurately, you must measure the length on you ruler with the help of a pair of compasses. Then the compass point must be positioned on B and the position of C must be indicated with a pencil mark.
• Construction:

4. Construct each of the following triangles:

4.2 $\Delta$ PQR with QR = 58 mm, P $\hat{Q}$ R = 62° and Q $\hat{P}$ R = 69°.

Measure:

1. PQ = mm
2. $\hat{R}$ =

4.2 Isosceles $\Delta$ ABC with BC = 42 mm, AB = AC and $\hat{B}$ = 63°.

Measure:

a) PQ = mm

Activity 2

Bisecting any given line or angle

[lo 3.4, 3.5, 4.7]

1. Bisecting a given line AB :

• Measuring line segment AB (e.g. 40 mm).
• Using a pair of compasses, measure slightly more than half of the line(i.e. ± 22-25 mm).
• Position the point of the pair of compasses on A and make a pencil stroke below and above the line.
• Position the point of the compasses on B and draw another pencil stroke above and below the line.
• Connect the intersections of the pencil strokes.
• Name the point on line AB , P. P is the centre of line AB .

2. Now try the following:

• Draw line segment PQ = 70 mm.
• Bisecting line segment PQ , as in nr. 1 explained.

3. Bisect π ABC :

• Place the point of the pair of compasses on B .
• Draw an arc of any size as indicated.
• Position the point of the compass on the point where the two lines intersect and draw pencil lines inside the angle.
• Position the point of the compass on the other point of intersection and draw a line inside the angle, so that the two lines intersect.
• Connect $\hat{B}$ (angle B ) with the point where your pencil lines intersect.
• $\hat{B}$ 1 will have the same size as $\hat{B}$ 2 . Measure both angles. Are they equal?

4. Try the following:

• Draw D $\hat{E}$ F = 125°.
• Bisect D $\hat{E}$ F .

Activity 3

To construct a line perpendicular from a given point to another line

[lo 3.4, 3.5, 4.7]

1. Construct AD $$ BC .

• Place your compass point on A (you want to draw a perpendicular line on BC from A.)
• Make an arc on BC .
• Place the point of your compasses on the one point of intersection between the arc and BC. Draw a line below BC. Place the point of your compasses on the other point of intersection between the arc and BC and draw another line below BC , so that the two lines intersect.
• Connect A with the intersection of the two drawn lines.
• Mark the point of intersection D .
• AD will be perpendicular to BC . ( AD $$ BC .)