1. Review: -Construction of Bisected Segment and Bisected Angle USING: a)ruler b)compass c)blank sheets

2. ESSENTIAL QUESTION
What are Complementary and Supplementary Angles?

3. Vocabulary
Complementary Angles: two angles whose measure is 90°

4. Complementary Angles: two angles whose measure is 90°

5. VOCABULARY
Supplementary Angles: two angles whose measure is 180°

6. Supplementary Angles: two angles whose measure is 180°

7. Example 1
Identify Complements and Supplements
Determine whether the angles are complementary, supplementary, or neither. a. b. c. 7

8. complementary nor supplementary.
Example 1
Identify Complements and Supplements
Determine whether the angles are complementary, supplementary, or neither. a. b. c.
SOLUTION a.
supplementary. b.
complementary nor supplementary. c.
complementary. 8

9. Checkpoint
Identify Complements and Supplements
Determine whether the angles are complementary, supplementary, or neither. 1. 2. 3.

10. Checkpoint
Identify Complements and Supplements
Determine whether the angles are complementary, supplementary, or neither. 1.
ANSWER
neither 2.
ANSWER
complementary 3.
ANSWER
supplementary

11. Adjacent Angles: two angles that share a common vertex and a common side (ray).

12. Tell whether the numbered angles are adjacent or nonadjacent.
Example 2
Identify Adjacent Angles
Tell whether the numbered angles are adjacent or nonadjacent. a. b. c.
SOLUTION a.
1 and 2 are nonadjacent. b.
3 and 4 are adjacent. c.
Although 5 and 6 share a common vertex,
they do not share a common side. Therefore,
5 and 6 are nonadjacent. 12

13. Complements: their sum = 90°
Supplements: their sum = 180°

14. A is a complement of C, and mA = 47°. Find mC. a.
Example 3
Measures of Complements and Supplements
A is a complement of C, and mA = 47°. Find mC. a. b.
P is a supplement of R, and mR = 36°. Find mP.
SOLUTION a. b.
mA + mC = 90°
mP + mR = 180°
47° + mC = 90°
mP + 36° = 180°
47°+ mC – 47° = 90° – 47°
mP + 36° – 36° = 180° – 36°
mC = 43°
mP = 144° 14

15. Vocabulary
Theorem: a true statement that follows from other true statements.
Congruent Complements Theorem: If two angles are complementary to the same angle, then they are congruent.

16. In the diagram, m10 + m11 = 90°, and m11 + m12 = 90°.
Checkpoint
Use a Theorem
In the diagram, m10 + m11 = 90°, and
m11 + m12 = 90°.
Name a pair of congruent angles. Explain your reasoning.
ANSWER
10  12; 10 and 12 are both complementary to 11, so 10  12 by the Congruent Complements Theorem.

17. Theorem: a true statement that follows from other true statements.
Congruent Supplements Theorem

18. Theorem: a true statement that follows from other true statements.
Congruent Supplements Theorem : If two angles are supplementary to the same angle, then they are congruent

19. 7 and 8 are supplementary, and 8 and 9 are supplementary.
Example 4
Use a Theorem
7 and 8 are supplementary, and 8 and 9 are supplementary.
Are angles 8 & 9 congruent?
SOLUTION
7 and 9 are both supplementary to 8.
So, by the Congruent supplements Theorem, 7  9. 19

20. Example 4
Use a Theorem
Example:
SOLUTION 20

21. Hw: Worksheet 2.3B
Quiz Friday