Bisecting of Angles

CONTENT

DEFINITION OF ANGLES

TYPES OF ANGLES

BISECTION AND CONSTRUCTION OF ANGLES.

ANGLES

An angle is formed when two straight lines intersect or meet at a point.

The sum of angle at the centre of a complete circle is 360^0.

TYPES OF ANGLES

1. Acute angles: – These are angles that are less than 90⁰.
2. Right angle: – This is an angle that is equal to 90⁰.
3. Obtuse angles: – These are angles that are greater than 90⁰ but less than 180⁰.
4. Reflex angles: – These are angles that are greater than 180⁰ but less than 360⁰.
5. Complementary angles: – These are angles that sum up to 90⁰.
6. Supplementary angles: – These are angles that sum up to 180⁰.

EVALUATION

1. Define an angle.
2. Mention five types of angle and describe them.

CONSTRUCTION OF ANGLES

The following are several ways of constructing or drawing angles:

• Using a setsquare
• Using a combination of setsquares
• Using a protractor
• Using a pair of compasses

HOW TO CONSTRUCT ANGLES USING SETSQUARE

Standard angles are angles 30⁰,45⁰, 60⁰ and 90⁰. These angles can be drawn by simply using a setsquare. The method is simply choosing the appropriate setsquare that has the angle that is to be drawn. Thus 30⁰-60⁰ setsquare is used to draw 30⁰, 60⁰ and 90⁰. Similarly, the 45-45 setsquare is used to draw 45⁰ and 90⁰.

EVALUATION

With the aid of a set square construct the following angle: i)90⁰ ii) 60⁰ iii)45⁰

COMBINATION OF SETSQUARES

Setsquares can be combined to construct the following angles:

1. To construct 75⁰, combine 45⁰ and 60⁰ setsquares

          180⁰– (60⁰ +  45⁰)= 75⁰

2. To construct 135⁰, combine 45⁰ and 90⁰

         45⁰+ 90⁰ = 135⁰ 

3. To construct 105⁰, combine 60⁰ and 45⁰

         45⁰+ 60⁰ = 135⁰

EVALUATION

1. Combine the sets-square to construct angles75⁰ and 135⁰.
2. Construct angle 60^o

HOW TO DRAW AN ANGLE USING A PROTRACTOR

Procedure

1. Place the protractor on the line from which the angle is to be formed. The baseline marked O at one end and, 180 marked at the other end.
2. Set the centre of the protractor to start from where the vertex of the angle will be.
3. Mark the required degree of the angles to be drawn.
4. Use a straight line to join the marked point at the angle to the point vertex of the angle

EVALUATION

1. Measure the following angles using your protractor

a) 88⁰      b)170⁰        c)275⁰             d) 300⁰        e)15⁰

2. Construct angle 30^o

How to construct Angles Using a Pair of Compasses  

60⁰

Procedure

1. Draw a straight line and mark the centre O.
2. From O, using a convenient radius at point A draw an arc (almost a quadrant).
3. With same radius draw another arc to intersect the first arc at C.
4. Draw a line from O through the point of intersection.

The angle formed is 60⁰

90⁰

Procedure

1. Draw a straight line and mark the centre O.
   1. From O draw a semicircle to touch the straight line at A and B.
   1. From A, with longer radius, draw an arc at the centre up.
   1. From B, with longer radius, draw an arc at the centre up to intersect at C.
   1. Draw a line from O through C.

The angle COA and COB is 90⁰

BISECTION OF ANGLES

To bisect a given angle

1. Draw a given angle ABC.
2. With centre B and any convenient radius draw an arc to cut AB to D and BC at E.
3. With centre A¹ and any small radius an arc.
4. With centre E and the same radius draw an arc to intersect the previous one at F.
5. Join BD, BD bisects angle ABC, i.e. angle ABD= DBC.
6. Use a protractor to check angles ABF and CBF.

The following angles can be constructed by bisection:

• 30⁰ can be constructed by bisecting 60⁰
• 15⁰ can be constructed by bisecting 30⁰
• 12.5⁰ can be constructed by bisecting 15⁰
• 45⁰ can be constructed by bisecting 90⁰
• 22.5⁰ can be constructed by bisecting 45⁰

READING ASSIGNMENT

‘Read about TRIANGLES’

1. MELROSE, Basic Science and Technology, Book 2 page 77-79
   1. NERDC-BASIC TECHNOLOGY, BOOK 2, page 46- 51

WEEKEND ASSIGNMENT

1. The angle that FC makes when constructed perpendicular with line AB is _______ (a) 180⁰ (b) 270⁰ (c) 90⁰ (d) 120⁰
2. The line FC is called __________  (a) vertical (b) perpendicular  (c) Horizontal (d) incline
3. Which of the following drawing materials cannot be used to construct a straight line? (a) Compass (b) protractor (c) Ruler (d) pencils
4. Angles that sum up to 180⁰ is called __________ (a) supplementary (b) complementary (c) Reflex (d) obtuse
5. The line for all visible outlines is called ____________ (a) Thin continuous line (b) Thick continuous line (c) short dashes (d) Zig – Zag lines.

THEORY

1. With the aid of a protractor measure the following angles

(a)15⁰ (b)70⁰ (c)150⁰ (d)220⁰ (e)300⁰. With the aid of compasses and a ruler construct angle 60⁰ and 30⁰