Angles.ppt No 2 topic.ppt

1. MATHEMATICS 7

2. Contents
• Recap the terms
• Angles in daily life
• What is an angle?
• Naming an angle
• Interior and exterior of an angle
• Measurement of angle
• Types of angle: Right angle
Obtuse angle
Acute angle
Straight angle
• Test Yourself - 1
• Congruent angles
• Pairs of angles: Types
• Test Yourself - 2
• Pairs of angles formed
by a transversal
• Test Yourself - 3

3. Point
An exact location on a plane is
called a point.
Line
Line
segment
Ray
A straight path on a plane,
extending in both directions
with no endpoints, is called a
line.
A part of a line that has two
endpoints and thus has a
definite length is called a line
segment.
A line segment extended
indefinitely in one direction
is called a ray.
Recap Geometrical Terms

4. If we look around us, we will see angles
everywhere.
Angles In Daily Life

5. Common
endpoint
B C
B
A
Ray BC
Ray BA
Ray BA and BC are two non-collinear rays
When two non-collinear rays join with a
common endpoint (origin) an angle is
formed.
What Is An Angle ?
Common endpoint is called the vertex of the angle. B is the
vertex of .
Ray BA and ray BC are called the arms of ABC.

6. Fact: We can also think of an angle formed by rotating one
ray away from its initial position.

7. To name an angle, we name any point on
one ray, then the vertex, and then any point
on the other ray.
For example: ÐABC or ÐCBA
We may also name this angle only by the
single letter of the vertex, for example B.
A
B
C
Naming An Angle

8. An angle divides the points on the
plane into three regions:
A
B
C
F
R
P
T
X
Interior And Exterior Of An Angle
• Points lying on the angle
(An angle)
• Points within the angle
(Its interior portion. )
• Points outside the
angle (Its exterior
portion. )

9. Angles are accurately measured in
degrees.
Protractor is used to measure and
draw angles.
Measurement Of An Angle

10. There are four main types of angles.
Straight angle
Right
angle
Acute
angle
Obtuse
angle
A
B C
A
B C
A
B C
B
A C
Types Of Angles

11. Right angle: An angle whose measure
is 90 degrees.
Right Angle Acute Angle
Straight Angle Obtuse Angle

12. Examples Of Right Angle

13. Obtuse angle: An angle whose measure
is greater than 90 degrees.
Right Angle Acute Angle
Straight Angle Obtuse Angle

14. Examples Of Obtuse Angle

15. Acute angle: An angle whose measure
is less than 90 degrees.
Right Angle Acute Angle
Straight Angle Obtuse Angle

16. Examples Of Acute Angle

17. Straight angle: An angle whose
measure is 180 degrees.
Right Angle Acute Angle
Straight Angle Obtuse Angle

18. Examples Of Straight Angle

19. A
B
C
D
E
F
P
Q R
Which of the angles below is a right angle, less than a right
angle and greater than a right angle?
Right angle
Greater than a right angle
Less than a right angle
1. 2.
3.

20. Two angles that have the same
measure are called congruent angles.
Congruent angles have the
same size and shape.
A
B
C
300
D
E
F
300
D
E
F
300
Congruent Angles

21. Pairs Of Angles : Types
• Adjacent angles
• Vertically opposite angles
• Complimentary angles
• Supplementary angles
• Linear pairs of angles

22. Adjacent Angles
Two angles that have a common vertex and a common ray
are called adjacent angles.
C
D
B
A
Common ray
Common vertex
Adjacent Angles ABD and DBC
Adjacent angles do not overlap each other.
D
E
F
A
B
C
ABC and DEF are not adjacent angles

23. Vertically Opposite Angles
Vertically opposite angles are pairs of angles
formed by two lines intersecting at a point.
APC = BPD
APB = CPD
A
D
B
C
P
Four angles are formed at the point of intersection.
Point of intersection ‘P’ is the common
vertex of the four angles.
Vertically opposite angles are congruent.

24. If the sum of two angles is 900, then they are
called complimentary angles.
600
A
B
C
300
D
E
F
ABC and DEF are complimentary because
600 + 300 = 900
ABC + DEF
Complimentary Angles

25. 700
D
E
F
300
p
Q
R
If the sum of two angles is more than
900 or less than 900, then they not
complimentary angles.
DEF and PQR are not complimentary because
700 + 300 = 1000
DEF + PQR

26. If the sum of two angles is 1800 then they
are called supplementary angles.
PQR and ABC are supplementary, because
1000 + 800 = 1800
R
Q
P
A
B
C
1000
800
PQR + ABC
Supplementary Angles

27. If the sum of two angles is more than 1800
or less than 1800, then they are not
supplementary angles.
DEF and PQR are not supplementary because
ABC + DEF
1100 + 800 = 1900
D
E
F
800
C
B
A
1100

28. Two adjacent supplementary angles
are called linear pair of angles.
A
600 1200
P
C D
600 + 1200 = 1800
APC + APD
Linear Pair Of Angles

29. Name the adjacent angles and linear pair of angles in the
given figure:
Adjacent angles:
ABD and DBC
ABE and DBA
Linear pair of angles:
EBA, ABC C
D
B
A
E
600
300
900
EBD, DBC
C
D
B
A
E
600
300
900

30. Name the vertically opposite angles and adjacent angles in
the given figure:
A
D
B
C
P
Vertically opposite angles: APC and BPD
APB and CPD
Adjacent angles: APC and CPD

31. A line that intersects two or more lines at different points is
called a transversal.
Line L (transversal)
B
A
Line M
Line N
D
C
P
Q
G
F
Pairs Of Angles Formed by a Transversal
Line M and line N are parallel lines.
Line L intersects line M an
med at point P and another f angles our at point Q by the
transversal L.
Eight angles are formed in all by the transversal L.

32. Pairs Of Angles Formed by a Transversal
• Corresponding angles
• Alternate angles
• Interior angles

33. Corresponding Angles
When two parallel lines are cut by a transversal, pairs of
corresponding angles are formed.
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.
GPB = PQE
GPA = PQD
BPQ = EQF
APQ = DQF
Line M
B
A
Line N
D E
L
P
Q
G
F
Line L

34. Alternate Angles
Alternate angles are formed on opposite sides of the
transversal and at different intersecting points.
Line M
B
A
Line N
D E
L
P
Q
G
F
Line L
BPQ = DQP
APQ = EQP
Pairs of alternate angles are congruent.
Two pairs of alternate angles are formed.

35. The angles that lie in the area between the two parallel lines
that are cut by a transversal, are called interior angles.
A pair of interior angles lie on the same side of the
transversal.
The measures of interior angles in each pair add up to 1800.
Interior Angles
Line M
B
A
Line N
D E
L
P
Q
G
F
Line L
600
1200
1200
600
BPQ + EQP = 1800
APQ + DQP = 1800

36. Name the pairs of the following angles formed by a
transversal.
Line M
B
A
Line N
D E
P
Q
G
F
Line L