Congruent Supplements and Complements

1
Congruent Supplements and Complements

• Section 2.4
• By Ellen Wildner

2
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

3
Review

• Complementary Angles
• 2 angles are complementary if the sum of their
  measures is
• For Ex.
• therefore must equal

4
Review Continued

• Supplementary Angles
• 2 angles are supplementary if the sum of their
  measures is
• For Ex.
• therefore must equal

5
Now we beginTheorem 4

• Theorem 4 If angles are supplementary to the
  same angle, then they are congruent.

For ex. In the diagram to the right is
supplementary to , and is also
supplementary to
Therefore we can prove that
6
Sample Problem Thm 4.

• Given is supp. to
• is supp. to
• Prove

Statements
Reasons
1. is supp. to
1. Given
2. is supp. to
2. Given
3.
3.Given
4.
4. If angles are supplementary to angles they
are
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Theorem 5

• Theorem 5 If angles are supplementary to
  congruent angles, then they are
  congruent.

For ex. It is given that is supp. to
is supp. to And that
Therefore we can prove that
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Sample Problem Thm. 5

• Given supp. of
• supp. of
• Conclusion

Statements
Reasons
1. supp. of 1. Given
2. supp. of 2. Given
3. 3.
Given
4. 4.
If 2 angles are supp. To angles they
are
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Theorem 6

• Theorem 6 If angles are complementary to the
  same angle, then they are

For ex. It is given that comp and
comp
Therefore we can prove that
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Sample Problem Thm. 6

• Given comp
• comp
• Conclusion

Statements
Reasons
1. comp 1.
Given
2. comp 2.
Given
3.
3. If angles are complementary to the
same angle, then they are
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Theorem 7

• Theorem 7 If angles are complementary to
  congruent angles, then they are congruent.

For ex. It is given that comp and
comp
Therefore we can prove that
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Sample Problem Thm. 7

• Given comp to
• comp to
• Conclusion

Statements Reasons
1. comp to 1. Given
2. comp to 2. Given
3. 3.
Given
4. 4.
If angles are complementary to
congruent angles, then they are
congruent.
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Practice Problems

• Given is comp to
• is comp to
• Conclusion

Statements Reason
1. is comp to 1. Given
2. is comp to 2. Given
3. 3. If
angles are complementary to the
same angle they are congruent
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Practice Problems

• Applying skills
• Given is comp to
• a. 49
• b. 131
• c. 49
• d. 41
• e. 139
• 41
• 139

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Practice Problems

• Given Diagram as shown
• Prove

Statements Reasons
1. 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
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Practice Problems

• Given is supp to
• is supp to
• Conclusion

17
Works Cited

• "Complementary, Supplementary, and Vertical
  Angles." Algrebra Labs. 29 May 2009
  lthttp//www.algebralab.org/lessons/lesson.aspx?fi
  leGeometry _AnglesComplementarySupplementaryVerti
  cal.xmlgt.
• Rhoad, Richard, George Milauskas, and Robert
  Whipple. Geometry for Enjoyment and Challenge.
  Boston McDougal Littell, 1997. 76- 81.