Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D...
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Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D is a point interior to angle ABC, then A D B C DBC ABD ABC m m m
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Transcript of Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D...
Introduction to Geometry – Complimentary / Supplementary Angles
Angle Addition Postulate – If D is a point interior to angle ABC, then
A D
B C
DBC ABDABC mmm
Introduction to Geometry – Complimentary / Supplementary Angles
Angle Addition Postulate – If D is a point interior to angle ABC, then
A D
B C
DBC ABDABC mmm
A
50°75°
In this example :
125 ABC
7550 ABC
m
m
Introduction to Geometry – Complimentary / Supplementary Angles
Angle Addition Postulate – If D is a point interior to angle ABC, then
A D
B C
DBC ABDABC mmm
A
50°75°
In this example :
125 ABC
7550 ABC
m
m
A straight angle is formed by two rays going away from each other. It measures 180°.
180°
B C
Introduction to Geometry – Complimentary / Supplementary Angles
Angle Addition Postulate – If D is a point interior to angle ABC, then
A D
B C
DBC ABDABC mmm
A
50°75°
In this example :
125 ABC
7550 ABC
m
m
A straight angle is formed by two rays going away from each other. It measures 180°. Draw a third ray and you have a linear pair. This linear pair forms a straight line, they are supplementary angles and add up to 180°.
B A C
D
Introduction to Geometry – Complimentary / Supplementary Angles
Supplementary Angles – formed by a linear pair and add up to 180°
Introduction to Geometry – Complimentary / Supplementary Angles
Supplementary Angles – formed by a linear pair and add up to 180°
EXAMPLE : Let’s fill in the table with the missing supplementary angle.
Angle 1 Angle 2
60°
These pairs should all add up to 180°
Introduction to Geometry – Complimentary / Supplementary Angles
Supplementary Angles – formed by a linear pair and add up to 180°
EXAMPLE : Let’s fill in the table with the missing supplementary angle.
Angle 1 Angle 2
60° 120 °
These pairs should all add up to 180°
Introduction to Geometry – Complimentary / Supplementary Angles
Supplementary Angles – formed by a linear pair and add up to 180°
EXAMPLE : Let’s fill in the table with the missing supplementary angle.
Angle 1 Angle 2
60° 120°
155°
These pairs should all add up to 180°
Introduction to Geometry – Complimentary / Supplementary Angles
Supplementary Angles – formed by a linear pair and add up to 180°
EXAMPLE : Let’s fill in the table with the missing supplementary angle.
Angle 1 Angle 2
60° 120°
155° 25°
These pairs should all add up to 180°
Introduction to Geometry – Complimentary / Supplementary Angles
Supplementary Angles – formed by a linear pair and add up to 180°
EXAMPLE : Let’s fill in the table with the missing supplementary angle.
Angle 1 Angle 2
60° 120°
155° 25°
42° *174° *76° *
These pairs should all add up to 180°
See if you can get the last three on your own before moving to the next page…
Introduction to Geometry – Complimentary / Supplementary Angles
Supplementary Angles – formed by a linear pair and add up to 180°
EXAMPLE : Let’s fill in the table with the missing supplementary angle.
Angle 1 Angle 2
60° 120°
155° 25°
42° 138°
174° 6°
76° 104°
These pairs should all add up to 180°
See if you can get the last three on your own before moving to the next page…
Introduction to Geometry – Complimentary / Supplementary Angles
Complementary Angles – two angles that form a right angle and add up to 90°
40°
50°
Introduction to Geometry – Complimentary / Supplementary Angles
Complementary Angles – two angles that form a right angle and add up to 90°
EXAMPLE : Let’s fill in the table with the missing complementary angle.
Angle 1 Angle 2
60°
These pairs should all add up to 90°
Introduction to Geometry – Complimentary / Supplementary Angles
Complementary Angles – two angles that form a right angle and add up to 90°
EXAMPLE : Let’s fill in the table with the missing complementary angle.
Angle 1 Angle 2
60° 30°
These pairs should all add up to 90°
Introduction to Geometry – Complimentary / Supplementary Angles
Complementary Angles – two angles that form a right angle and add up to 90°
EXAMPLE : Let’s fill in the table with the missing complementary angle.
Angle 1 Angle 2
60° 30°
45°
These pairs should all add up to 90°
Introduction to Geometry – Complimentary / Supplementary Angles
Complementary Angles – two angles that form a right angle and add up to 90°
EXAMPLE : Let’s fill in the table with the missing complementary angle.
Angle 1 Angle 2
60° 30°
45° 45°
These pairs should all add up to 90°
Introduction to Geometry – Complimentary / Supplementary Angles
Complementary Angles – two angles that form a right angle and add up to 90°
EXAMPLE : Let’s fill in the table with the missing complementary angle.
Angle 1 Angle 2
60° 30°
45° 45°
27° *79° *16° *
These pairs should all add up to 90°
See if you can get the last three on your own before moving to the next page…
Introduction to Geometry – Complimentary / Supplementary Angles
Complementary Angles – two angles that form a right angle and add up to 90°
EXAMPLE : Let’s fill in the table with the missing complementary angle.
Angle 1 Angle 2
60° 30°
45° 45°
27° 63°
79° 11°
16° 74°
These pairs should all add up to 90°
See if you can get the last three on your own before moving to the next page…
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines and on the opposite side
A
E
D
CB
AEDBEC and
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines and on the opposite side
A
E
D
CB
AEDBEC and
CEDBEA and
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines and on the opposite side
A
E
D
CB
AEDBEC and
CEDBEA and
Vertical angles are also congruent
CEDBEA
AEDBEC
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angleFind the partner for the given angle to make a vertical angle pair.
Q
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA ?
Find the partner for the given angle to make a vertical angle pair.
Q
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA ∟CQD
Find the partner for the given angle to make a vertical angle pair.
Q
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA ∟CQD
∟FQC
Find the partner for the given angle to make a vertical angle pair.
Q
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA ∟CQD
∟FQC ∟AQE
Find the partner for the given angle to make a vertical angle pair.
Q
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA ∟CQD
∟FQC ∟AQE
∟FQD
Find the partner for the given angle to make a vertical angle pair.
Q
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA ∟CQD
∟FQC ∟AQE
∟FQD ∟BQE
Find the partner for the given angle to make a vertical angle pair.
Q
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA = 50° ∟CQD = ?
∟FQC ∟AQE
∟FQD ∟BQE
Complete the table with the missing measurement.
Q50°
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA = 50° ∟CQD = 50°
∟FQC ∟AQE
∟FQD ∟BQE
Q50°50°
Complete the table with the missing measurement.
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA = 50° ∟CQD = 50°
∟FQC = 38° ∟AQE = ?
∟FQD ∟BQE
Q
38°
Complete the table with the missing measurement.
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA = 50° ∟CQD = 50°
∟FQC = 38° ∟AQE = 38°
∟FQD ∟BQE
Q
38°
38°
Complete the table with the missing measurement.
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA = 50° ∟CQD = 50°
∟FQC = 38° ∟AQE = 38°
∟FQD = 136° ∟BQF = ?
Q
136°
Complete the table with the missing measurement.
Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CBF
Given angle Vertical angle
∟BQA = 50° ∟CQD = 50°
∟FQC = 38° ∟AQE = 38°
∟FQD = 136° ∟BQF = 44°
Q
136°
Complete the table with the missing measurement.
44°
Linear pair
