angles – all you need to know!. contents recap the terms angles in daily life what is an angle?...
TRANSCRIPT
Angles – all you need to know!
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
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.
Using your spiral notebook – write the definitions and draw an example of each of the following angles
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
• Complementary 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 complementary angles.
600
A
BC
300
D
EF
ABC and DEF are complementary because
600 + 300 = 900
ABC + DEF
Complementary Angles
700
D
EF
300
p
QR
If the sum of two angles is more than 900 or less than 900, then they not complementary angles.
DEF and PQR are not complementary because
700 + 300 = 1000
DEF + PQR
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
working with your partner solve the following
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
900
EBD, DBC
C
D
B
A
E
600
30
Name the vertically opposite angles and adjacent angles in the given figure:
A
DB
C
P
Vertically opposite angles: APC and BPD
APB and CPD
Adjacent angles: APC and CPD
APB and BPD
Using your Frayer Template forms write definitions and examples of each of the terms on the next slide
now working with your partner complete the following
Homework for this evening Page 378 Problems 8 through 22 even Show all work – write reasoning if work not
required.
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 & line N at point P & 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.
BALine M
Line NDC
P
Q
G
F
Pairs Of Angles Formed by a Transversal
Can you explain why?
Eight angles are formed in all by the transversal L.
All angles labeled 1 are equal
1
1
1
1
All angles labeled 2 are equal
2
2
2
2
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
Homework
page 384 9 through 24 all
Do not forget to show all work or write reason if work not required.
Begin now please.