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

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

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

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

5. There are four main types of angles.
Right angle
Acute angle
Obtuse angle A B C A B C A B C
Straight angle B A C

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

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

8. Adjacent Angles ABC and DEF are not 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 D E F A B C
Adjacent Angles ABD and DBC
Adjacent angles do not overlap each other.
ABC and DEF are not adjacent angles

9. Vertically Opposite Angles
Vertically opposite angles are pairs of angles formed by two lines intersecting at a point. A D B C
ÐAPC = ÐBPD P
ÐAPB = ÐCPD
Four angles are formed at the point of intersection.
Vertically opposite angles are congruent.
Point of intersection ‘P’ is the common vertex of the four angles.

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

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

12. Two adjacent supplementary angles are called linear pair of angles.
1200
600 C D P
ÐAPC + ÐAPD
= 1800

13. Adjacent angles: ÐAPC and ÐCPD
Name the vertically opposite angles and adjacent angles in the given figure: A D B C P
Vertically opposite angles: ÐAPC and ÐBPD
Adjacent angles: ÐAPC and ÐCPD
ÐAPB and ÐCPD
ÐAPB and ÐBPD

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

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

16. Corresponding Angles ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF
When two parallel lines are cut by a transversal, pairs of corresponding angles are formed.
Line M B A
Line N D E L P Q G F
Line L
ÐGPB = ÐPQE
ÐGPA = ÐPQD
ÐBPQ = ÐEQF
ÐAPQ = ÐDQF
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.

17. Alternate Angles ÐBPQ = ÐDQP ÐAPQ = ÐEQP
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
ÐBPQ = ÐDQP
ÐAPQ = ÐEQP
Two pairs of alternate angles are formed.
Pairs of alternate angles are congruent.

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

19. The Department of Research
The End
Created by:
The Department of Research
Bombay Cambridge Gurukul