1. ANGLE RELATIONSHIPS

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. 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

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

5. 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
Common endpoint is called the vertex of the angle. B is the vertex of ÐABC.
Ray BA and BC are two non-collinear rays
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. 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.

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

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

10. 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

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

12. Examples Of Right Angle

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

14. Examples Of Obtuse Angle

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

16. Examples Of Acute Angle

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

18. Examples Of Straight Angle

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

20. 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.

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

22. 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
ABC and DEF are not adjacent angles
Adjacent angles do not overlap each other.

23. 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.

24. 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

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

26. 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

27. ÐDEF and ÐPQR are not supplementary because
Contd….
If the sum of two angles is more than or less than 1800, then they are not supplementary angles. C B A
1100 D E F
800
ÐDEF and ÐPQR are not supplementary because
ÐABC + ÐDEF
= 1900

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

29. ÐABD and ÐDBC Test Yourself 2 ÐABE and ÐDBA ÐEBA, ÐABC ÐEBD, ÐDBC
Name the adjacent angles and linear pair of angles in the given figure:
Adjacent angles: C D B A E
600
300
900 C D B A E
600
300
900
ÐABD and ÐDBC
ÐABE and ÐDBA
Test Yourself 2
Linear pair of angles:
ÐEBA, ÐABC
ÐEBD, ÐDBC

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

31. 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
Line N P Q B A D C
Four angles are formed at point P and another four at point Q by the transversal L.
Line L intersects line M and line N at point P and Q.
Line M and line N are parallel lines.
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 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.

34. 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.

35. 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.

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
Alternate angles
Interior angles
Corresponding angles