modul lines and angle 1
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LINES AND ANGLE 1
LINES AND ANGLE 1
MEASURING ANGLES USING A PROTRACTOR
PROTRACTORe.g: Measure the angle in diagram below.
The steps to measure an unknown angle :
Place the centre of the protractor on vertex B
Adjust the base line so that it is aligned with the line BC
Read the value of from the inner scale
Solution :
EXERCISEMeasure all of angles in diagram below.
1.
2.
3.
4.
DRAWING ANGLES USING A PROTRACTOR
E.g:
a. How to draw an angle ABC which measures ?
Draw a straight horizontal straight line BC. Mark point B as the vertex
Place the centre of the protractor at vertex B and adjust the base line so that it is aligned with the line BC
Find the angle on the protractor scale and mark point A
Remove the protractor and draw a straight line from point B to point A
Label
b. Draw a reflex angle
Solution:
EXERCISE
Use a protractors to draw each of all angles below :
1.
2.
3.
4.
5.
6.
7.
8.
THE SUM OF ANGLEa. The sum of angles on a straight line is
b. The sum of angles at a point line is
E.g :
1. Calculate in the following diagram.
2. Find the value of x
EXERCISE
1. Calculate the value of p in each of the following figures
a.
Solution:
b.
Solution :
c.
Solution:
d.
Solution:
2. Determine the value of q in each of the following figures
a.
Solution:
b.
Solution :
c.
Solution:
d.
Solution:
PARALLEL LINE
PERPENDICULAR LINES
EXERCISE1. Determine if the pairs of straight lines below are parallel
a.
Solution :
b.
Solution:
2. Using a protractor, determine whether the line PQ is perpendicular to RS or not.a.
Solution :
b.
Solution:
INTERSECTING LINES
a. Vertically opposite angle
a and c are vertically opposite anglesb and d are vertically opposite angles
therefore, a = c and b = d
c. Supplementary angles
b. Complementary angles
d. Adjacent angles
EXERCISESolve all of questions below.
a. In the following diagram, lines PQ and
RS intersect at O. Determine the value of
P
Solution:
b. In the following diagram, find the value
of x
Solution:
c. p and q are complementary angles. Given that p = 550 , find the value of q.
Solution:
d. In the following figure, find the value of
p.
Solution:
LINES AND ANGLES
Lines
Angles
A
C
B
P
EMBED Equation.3
R
Q
EMBED Equation.3
D
F
E
U
EMBED Equation.3
T
S
L
EMBED Equation.3
M
N
B
EMBED Equation.3
EMBED Equation.3
Solution:
The sum of the given angles
= EMBED Equation.3
= EMBED Equation.3
Subtract this sum from EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
Solution:
x EMBED Equation.3
EMBED Equation.3
Two parallel lines are parallel if
They never meet or intersect
The perpendicular distance between two lines is the same at all points on either line
PQ is parallel to RS ( PQ // RS)
AB is parallel to CD ( AB // CD )
** // --- symbol for parallel
Two straight lines are perpendicular to each other if they intersect at a right angle (900 )
PQ is perpendicular to RS and vice versa
Two straight lines intersect if they meet only at one point
Line PQ intersect line RS at point T
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