congruent supplements and complements section 2.4 by: ellen wildner
TRANSCRIPT
Congruent Supplements and Complements
Section 2.4
By: Ellen Wildner
Objective or Goal
• After studying this section you will be able to…
– Prove angles congruent by using four new theorems that you will learn in this section
ReviewReview
• Complementary Angles– 2 angles are complementary if the sum of
their measures is
For Ex.
therefore must equal…
90
561 2
5690 34
Review Continued
• Supplementary Angles– 2 angles are supplementary if the sum of their
measures is
For Ex.
therefore must equal…
180
1121 2
112180 68
Now we begin…Theorem 4
Theorem 4: If angles are supplementary to the same angle, then they are congruent.
1
For ex. In the diagram to the right is supplementary to , and is also supplementary to
For ex. In the diagram to the right is supplementary to , and is also supplementary to
1
A
A2
A
2
Therefore we can prove that…
Therefore we can prove that…
21
Sample Problem Thm 4.
Given: is supp. to
is supp. to
Prove:
41 2
1
3
4
1 23 4
32
Statements Reasons
1. is supp. to 1 2
3 4
41
1. Given2. is supp. to 2. Given
3. 3.Given
4. 32 4. If angles are supplementary to angles they are
Theorem 5
Theorem 5: If angles are supplementary to congruent angles, then they are congruent.
B
A
For ex. It is given that is supp. to is supp. to And that
For ex. It is given that is supp. to is supp. to And that
BC DA
B D
CD
Therefore we can prove that…
Therefore we can prove that…
CA
Sample Problem Thm. 5
Given: supp. of
supp. of
Conclusion:
5 67 86 7
8
5 8 5 6 7 8
Statements Reasons
1. supp. of 1. Given5 62. supp. of 2. Given 7 83. 3. Given6 74. 4. If 2 angles are supp. To
angles they are 5 8
Theorem 6
Theorem 6: If angles are complementary to the same angle, then they are
A
For ex. It is given that comp and comp
For ex. It is given that comp and comp
BC
AA
B
C
Therefore we can prove that…
Therefore we can prove that…
CB
Sample Problem Thm. 6
Given: comp
comp
Conclusion:
1 232
2
31
1
2 3
Statements Reasons
1. comp 1. Given1 22. comp 2. Given2 33. 3. If angles are complementary to the
same angle, then they are 1
3
Theorem 7
Theorem 7: If angles are complementary to congruent angles, then they are congruent.
1
Therefore we can prove that…
Therefore we can prove that…
For ex. It is given that comp and comp
For ex. It is given that comp and comp
23 41
2
3
4
3 1
Sample Problem Thm. 7
Given: comp to
comp to
Conclusion:
1 23 43
31
2 41
2 34
Statements Reasons
1. comp to 1. Given2. comp to 2. Given
3. 3. Given 4. 4. If angles are complementary to
congruent angles, then they are congruent.
1 23 41 32 4
Practice Problems
Given: is comp to
is comp to
Conclusion:
HFG
E
E
E
HFG
G
G
HFG
F
H
G
Statements Reason
1. is comp to 1. GivenHFG
HFG
E
2. is comp to 2. Given
3. 3. If angles are complementary to the same angle they are congruent
E
Practice Problems
Applying skills
Given: is comp to
=
a. = 49
b. = 131
c. = 49
d. = 41
e. = 139
f. = 41
g. = 139
3
2 3
4 131 1 2 3 4
5678
2
8
7
6
5
1
Practice Problems
Given: Diagram as shown
Prove:
H
HFE
EFG
HFJ
GFJ
HFG
HFE
HFE
GFJ
GFJ HFG
Statements Reasons1. Diagram as shown 1. Given
2. is a straight 2. Assumed from diagram
3. is supp to 3. If 2 angles form a straigt angle they are supp
4. is a straight 4. Same as 2
5. is supp to 5. Same as 3
6. 6. If angles are supplementary to the same angle, they are congruent
E
F
G
J
Practice Problems
Given: is supp to
is supp to
Conclusion: 3
1
3
1
2 41
2
2
34
4
Works Cited
"Complementary, Supplementary, and Vertical Angles." Algrebra Labs. 29 May 2009
<http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_AnglesComplementarySupplementaryVertical.xml>.
Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Boston: McDougal Littell, 1997.
76- 81.