What's Your Angle?

What’s your angle?What’s your angle?

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

• Imagine• Imagine you lived in a two-dimensional world.

You could travel around, visit friends, but nothing in your world would have height.

• You could measure distances and angles. • You could travel fast or slow. You could go

forward, backwards or sideways. You could move in straight lines, circles, or anything so long as you never go up or down.

What is a Plane?

PointAn 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

If we look around us, we will see angles everywhere.

Angles In Daily Life

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 ABC.

Ray BA and ray BC are called the arms of ABC.

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

To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray.

For example: ABC or CBA

We may also name this angle only by the single letter of the vertex, for example B.

A

BC

Naming An Angle

An angle divides the points on the plane into three regions:

A

BC

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. )

Angles are accurately measured in degrees.

Protractor is used to measure and draw angles.

Measurement Of An Angle

There are four main types of angles.

Straight angle

Right angle Acute angle Obtuse angle

A

B C

A

B C

A

B C

BA C

Types Of Angles

Right angle: An angle whose measure is 90 degrees.

Right Angle Acute AngleStraight Angle Obtuse Angle

Examples Of Right Angle

Obtuse angle: An angle whose measure is greater than 90 degrees.

Right Angle Acute AngleStraight Angle Obtuse Angle

Examples Of Obtuse Angle

Acute angle: An angle whose measure is less than 90 degrees.

Right Angle Acute AngleStraight Angle Obtuse Angle

Examples Of Acute Angle

Straight angle: An angle whose measure is 180 degrees.

Right Angle Acute AngleStraight Angle Obtuse Angle

Examples Of Straight Angle

A

BC

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.

Two angles that have the same measure are called congruent angles.

Congruent angles have the same size and shape.

A

BC

300

D

EF

300

D

EF

300

Congruent Angles

Pairs Of Angles : Types

• Adjacent angles

• Vertically opposite angles

• Complimentary angles

• Supplementary angles

• Linear pairs of angles

Adjacent AnglesTwo 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

EF

A

B

C

ABC and DEF are not adjacent angles

Vertically Opposite AnglesVertically opposite angles are pairs of angles formed by two lines intersecting at a point.

APC = BPD

APB = CPD

A

DB

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.

If the sum of two angles is 900, then they are called complimentary angles.

600

A

BC

300

D

EF

ABC and DEF are complimentary because

600 + 300 = 900

ABC + DEF

Complimentary Angles

700

D

EF

300

p

QR

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

Contd….

If the sum of two angles is 1800 then they are called supplementary angles.

PQR and ABC are supplementary, because

1000 + 800 = 1800

RQ

PA

BC

1000 800

PQR + ABC

Supplementary Angles

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

EF

800

CB

A

1100

Contd….

Two adjacent supplementary angles are called linear pair of angles.

A

600 1200

PC D

600 + 1200 = 1800

APC + APD

Linear Pair Of Angles

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

Name the vertically opposite angles and adjacent angles in the given figure:

A

DB

C

P

Vertically opposite angles: APC and BPD

APB and CPDAdjacent angles: APC and CPD

APB and BPD

A line that intersects two or more lines at different points is

called a transversal.

Line L (transversal)

BALine M

Line NDC

P

Q

G

F

Pairs Of Angles Formed by a Transversal

Line M and line N are parallel lines.Line L intersects line M and line N at point P and Q.Four angles are formed at point P and another four at point

Q by the transversal L.Eight angles are formed in all by the transversal L.

Pairs Of Angles Formed by a Transversal

• Corresponding angles

• Alternate angles

• Interior angles

Corresponding AnglesWhen 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 MBA

Line ND E

L

P

Q

G

F

Line L

Alternate AnglesAlternate angles are formed on opposite sides of the transversal and at different intersecting points.

Line MBA

Line ND 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.

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 MBA

Line ND E

L

P

Q

G

F

Line L

6001200

1200600

BPQ + EQP = 1800

APQ + DQP = 1800

Name the pairs of the following angles formed by a transversal.

Line MBA

Line ND E

P

Q

G

F

Line L

Line MBA

Line ND E

P

Q

G

F

Line L

Line MBA

Line ND E

P

Q

G

F

Line L

500

1300