NOTES FOR MATHEMATICS TOPICS

MATHEMATICS - FORM 1

LINES AND ANGLES

ANGLES
A) Identifying an Angle
Angle is formed by two straight lines that meet
at a point called the vertex.

For example : -
     

In the figure above,

(a) AOB is an angle.
(b) OA and OB are called the arms of the angle.
(c) O is the vertex, that is the point where the two
     arms meet.


B) Naming an angle
An angle can be named by using one letter
or three letters.

For example :-
     




C) Measuring Angles
1. Angles are measured in units called degrees
    ( ⁰ ).
2. To measure an angle, we can use an instru-
    ment called the protractor as shown below.

         

3. Note that if we read from left to right ( clockwise
    direction ), we use the inner scale.
4. To measure an angle less than 180⁰, <KLM, follow
    the steps below.

 Method 1 :
         

    Step 1
    Place the protractor that its centre is on the vertex.

    L. Adjust the protractor until its base line corresponds
        with the arm LM.

        

    Step 2
    Read the value of <KLM using the inner scale.
    Therefore, <KLM = 30⁰.

    Method 2 :
        

    Step 1
    Place the protractor so that its centre is on the
    vertex L. Adjust the protractor until its base line
    corresponds with the arm LK.

    

    Step 2
    Read the value of  <KLM using the outer scale.

    Therefore, .KLM = 30⁰

5. To measure an angle which is more than 180⁰,
    follow the steps below :
    To measure <STU

    

    Step 1
    Produce the arm ST to V and measure <STV.
    <STV = 180⁰

    

    Step 2
    Place and adjust the protractor as shown to
    measure <VTU.

    

    Step 3
    <STU = <STV + <VTU
               =  180⁰ + 20⁰
               = 200⁰

    

D) Identifying the Different Types of Angles

The table below shows the different types of angles.



E) Determining the Sum of Angles on a
    Straight Line 

1. Use a protractor to measure the angles on the
    straight line.

Worked Example 4
Using a protractor, measure the angles on the
straight line KLM. Then, find the sum of the
angles in each case.

(a)                                           (b)
          

Solution

(a) x = 120⁰ , y = 60⁰
     x + y = 120⁰ + 60⁰
               = 180⁰

(b) p = 40⁰ , q = 90⁰ , r = 50⁰
      p + q + r = 40⁰ + 90⁰ + 50⁰ 
                      = 180

2. In general, the sum of the angles on a straight
    line is 180⁰.

    For example :-

          

    AOB is a straight line.
    x + y + z = 180⁰

E) Determining the Sum of Angles in
     One Whole Turn

1. A protractor is used to measure the angles
    at a point.

Worked Example 5
Use a protractor to measure the angles in the
figures. Then, find the sum of the angles in each
case.

(a)                                (b)
               

Solution

(a) x = 110⁰ , y = 250⁰
     x + y = 110⁰ + 250⁰
               = 360⁰

(b) p = 130⁰ , q = 60⁰ , r = 70⁰ , s = 100⁰
     p + q + r + s = 130⁰ + 60⁰ + 70⁰ + 100⁰
                            = 360⁰

2. In general, the sum of the angles that formed
    one whole turn is 360⁰.

    For example :-

    

    a + b + c + d + e = 360   


PARALLEL LINES AND
PERPENDICULAR LINES

A) Determining Parallel Lines

1. Parallel lines are lines that will not meet
    however far they are produced either way.
2. They are at the same distance apart from
    one other

    For example :-

    (a)
          

          KL is parallel to RS or KL//RS

    (b)
        
 
         AB//CD

(c)
        

        EF//HG
        EH//FG


B) Determining Perpendicular Lines
1. If two straight lines intersect at 90 , we say the two
    lines are perpendicular to each other.



    For example :-