Construction

CONSTRUCTION

By : kasskassmaths

​General Mathematics Syllabus

Section # 8, Objectives ​2 - 3

Table of Contents

​Contents of a Geometry Pan - Slide 3

Constructing angles (90, 60, 120) - Slide 9

Bisecting Angles (getting 45, 30, 60) - Slide 23

Measuring Angles (using protractor) - Slide 43

Constructing line segments - Slide 44

Bisecting a line segment - Slide​ 49

Constructing Triangles - Slide ​52​

Past paper Questions to practice - Slide ​60

Geometry Pan

​This is a metallic container of geometric / construction tools used to measure and draw angles, shapes, lines etc. It assists in accuracy and neatness of those things. The following slides will show the different tools or equipment contained in a basic geometry pan.

1. Protractor

​Used to measure and construct / draw angles.

2. Compass

​A compass is a type of tool that is used to create geometric shapes. It can be used for drawing circles, arcs, and other geometric figures.

3. Divider

​It has two sharp points, in which one sharp point used as a centre, and the other sharp point is used for marking.

4. Ruler

​A ruler is a tool that is used to measure the length, width, and height of objects. It is a straight metal or plastic bar with markings on the edges that can be aligned and read as a standard distance. They have a straight edge and usually have markings for inches, centimeters, millimeters, or feet.

5. Set Squares

​These are the triangular pieces of plastic with some portion between them removed. There are two kinds of set squares. One has an angle of 45 degrees and the other has 30-60 degrees. The 45 degree set square has an angle of 90 degrees, and also 30/60 degree set square has a right angle. The 45 degrees set square is used to draw vertical lines. With the help of set squares, we can draw parallel lines, perpendicular lines, make some standard angles, and so on.

Constructing Angles

​1. Using a ruler, draw a line any length (not too long) and mark off a point A close to the starting of the line.

​2. Open the compass to any length and make a large arc cutting the line.

​3. Maintaining the same length in step 2, put the compass on the point of intersection between the arc and line then make an arc cutting the arc made in step 2.

​4. Maintaining the same length in steps 2 and 3, place a compass on the point of intersection between the two arcs and make another arc cutting the arc made in Step 2.

​5. Open the compass to any length ( not too small),  place it on the arc made in step 3 and draw another Arc in "space." 

​6. Maintaining the same length in Step 5, place the compass on the arc drawn in step 4 and cut or intersect the arc thrown in step 5.

​7. Using a ruler and pencil, draw a line from point A, passing through the point of intersection of the two Arcs.

​8. Label the angle 90°.

​9. Check back: measure the angle using the protractor.

​1. Using a ruler and pencil, Draw a line any length (preferably not too long).

​2. Mark a point close to the starting of the line with a pencil and call it A. 

​3. Open the compass to any length (preferably not too wide). Place the marker on A and draw a wide arc cutting the line. 

​4.Put the compass on the point of intersection between the line and arc, maintaining the same length from step 3. Draw a small arc through the arc made in step 3.

​5. Using the ruler, Draw a line from A through the point of intersection between the 2 arcs. 

​6. Label the angle 60 degrees.

​7. Checkback : Measure the angle using the protractor and see if the angle created is 60 degrees.

​1. Using a pencil and rule, draw a line any length and mark off a point A. 

​2. Open the compass to any length, place it on A and draw a large arc cutting the line.

​3. Maintaining the same length, place the compass on the point of intersection between the arc and line then make an arc on the large arc drawn in step 2.

​4. Maintaining the same length, Place the compass on the point of intersection between the 2 arcs and make another arc. 

​5. Using a pencil and ruler, draw a line from point A, passing through the arc drawn in step 4.

​6. Label the angle 120° 

7. Checkmark: measure the angle using the protractor.

Bisecting Angles

​1. Make a 60° angle

2. Open the compass to any length and place it on the point of intersection between the line and large arc. Make an arc in "space." 

​4. Draw a line from point A, passing through the point of intersection of the 2 arcs.

​3. Maintaining the same length from step 2, place the compass on the point of intersection between the two arcs and upward slopping line. Draw an arc that cuts the arc made in step 2.

5. Label the angle(s) 30°.

6. Check back : use the protractor to measure

​1. Construct a 90°.

​2. Place the compass on the point of intersection between the large Arc and line. Draw an arc in "space".

​3. Place the compass on your point of intersection between the vertical line and large arc and draw an arc cutting the arc made in Step 2

​4. Draw a line from A, passing through the 2 arcs made in step 3.

​5. Label the angle(s) 45°.

6. Check back : measure using the protractor.

​1. Construct a 120° angle.

​2. Open the compass to any length and place it on the point of intersection between the line and big arc.

​3. Maintaining the same length, place the compass on the point of intersection between the diagonally drawn line and small Arc and draw an arc to cut the one drawn in step 2. 

​4. Using a pencil and ruler draw a line from point A , passing through the point of intersection between the 2 arcs.

​5. Label the angle(s) 60°.

​

Measuring Angles using a protractor

​When measuring angles using a protractor the placing and positioning of the protractor is very important, as one can get a wrong angle measurement if this isn't considered.

Constructing line segments

​Steps (using an example) :

1.​Using a pencil and ruler, draw a line any length.

​​2. Mark off a point A.

3.Take the protractor & using a ruler as the measurement, open it to the desired length. (5cm in this e.g.)

​​​​4.​ Maintaining that length, place the protractor on A and make an arc cutting the line.

5. Label the point of intersection between the small arc and line, point B and label the line the desired length. (5cm in this e.g.)

Bisecting a line segment

​​​Steps(using an example):

1. Open the compass

to any length and

place it on the

starting point of the

line / line segment.

Draw arcs in 'space'

above and below the line.

​2. Maintaining the same length

in step one, place the compass

on the ending point of the line

segment and draw 2 large

arcs that cuts or intersects the arcs drawn in step 1.

​​3. Using a ruler and pencil draw a line

passing through the point of intersections

between the 2 pairs of arcs and through the line.

​

Constructing Triangles

Triangles are made up of angles and sides that vary according to the triangle to be drawn. When Constructing Triangles, the instructions given must be understood and followed exactly.

Note the angles (their size in degrees , position & names : A,B,C) and the sides (their length, position E.g side AB = 5cm)

​E.g. Using a ruler , protractor and compass only, Construct a triangle ABC with AB = 6cm, AC = 4cm and CAB (angle A) of 60 degrees. Show all construction lines. Measure and state the size of angle ABC (angle B) and side BC.

​Steps :

1. Construct the base line AB of 6cm.

2.​Construct angle CAB of 60 degrees.

3. ​Construct the line AC of 4cm.

​4.Connect point B to point C.

​5. Measure and State Angle ABC (angle B)

​

It's 40 degrees.​

6. ​Measure and State the length of the side BC.

​

Its 5.3cm​

Past Paper Questions to Practice

​June 2019 No. 3 (a).

June 2018 No. 3 (a)

​