Introduction to Geometry - Complimentary / Supplementary Angles

1. Introduction to Geometry – Complimentary / Supplementary Angles
Angle Addition Postulate – If D is a point interior to angle ABC, then
A D
B C
DBCABDABC mmm +=

2. Introduction to Geometry – Complimentary / Supplementary Angles
Angle Addition Postulate – If D is a point interior to angle ABC, then
A D
B C
DBCABDABC mmm +=
A
50°
75°
In this example :
°=
°+°=
125ABC
7550ABC
m
m

3. Introduction to Geometry – Complimentary / Supplementary Angles
Angle Addition Postulate – If D is a point interior to angle ABC, then
A D
B C
DBCABDABC mmm +=
A
50°
75°
In this example :
°=
°+°=
125ABC
7550ABC
m
m
A straight angle is formed by two rays going away from each other. It measures 180°.
180°
B C

4. Introduction to Geometry – Complimentary / Supplementary Angles
Angle Addition Postulate – If D is a point interior to angle ABC, then
A D
B C
DBCABDABC mmm +=
A
50°
75°
In this example :
°=
°+°=
125ABC
7550ABC
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

5. Introduction to Geometry – Complimentary / Supplementary Angles
Supplementary Angles – formed by a linear pair and add up to 180°

6. 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°

7. 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°

8. 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°

9. 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°

10. 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…

11. 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…

12. Introduction to Geometry – Complimentary / Supplementary Angles
Complementary Angles – two angles that form a right angle and add up to 90°
40°
50°

13. 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°

14. 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°

15. 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°

16. 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°

17. 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…

18. 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…

19. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB

20. 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

21. 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

22. 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
∠≡∠
∠≡∠

23. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angleFind the partner for the given
angle to make a vertical angle
pair.
Q

24. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA ?
Find the partner for the given
angle to make a vertical angle
pair.
Q

25. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA ∟CQD
Find the partner for the given
angle to make a vertical angle
pair.
Q

26. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA ∟CQD
∟FQC
Find the partner for the given
angle to make a vertical angle
pair.
Q

27. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA ∟CQD
∟FQC ∟AQE
Find the partner for the given
angle to make a vertical angle
pair.
Q

28. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA ∟CQD
∟FQC ∟AQE
∟FQD
Find the partner for the given
angle to make a vertical angle
pair.
Q

29. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA ∟CQD
∟FQC ∟AQE
∟FQD ∟BQE
Find the partner for the given
angle to make a vertical angle
pair.
Q

30. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA = 50° ∟CQD = ?
∟FQC ∟AQE
∟FQD ∟BQE
Complete the table with the
missing measurement.
Q
50°

31. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA = 50° ∟CQD = 50°
∟FQC ∟AQE
∟FQD ∟BQE
Q
50°50°
Complete the table with the
missing measurement.

32. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA = 50° ∟CQD = 50°
∟FQC = 38° ∟AQE = ?
∟FQD ∟BQE
Q
38°
Complete the table with the
missing measurement.

33. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA = 50° ∟CQD = 50°
∟FQC = 38° ∟AQE = 38°
∟FQD ∟BQE
Q
38°
38°
Complete the table with the
missing measurement.

34. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
Given angle Vertical angle
∟BQA = 50° ∟CQD = 50°
∟FQC = 38° ∟AQE = 38°
∟FQD = 136° ∟BQF = ?
Q
136°
Complete the table with the
missing measurement.

35. Introduction to Geometry – Complimentary / Supplementary Angles
Vertical Angles – angles formed by two intersecting lines
A
E
D
CB
F
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