Review Construction of Bisected Segment and Bisected Angle

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

ESSENTIAL QUESTION • What are Complementary and Supplementary Angles?

Vocabulary • Complementary Angles: two angles whose measure is 90°

• Complementary Angles: two angles whose measure is 90°

VOCABULARY • Supplementary Angles: two angles whose measure is 180°

• Supplementary Angles: two angles whose measure is 180°

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

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.

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

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

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

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.

• Complements: their sum = 90° • Supplements: their sum = 180°

Example 3 Measures of Complements and Supplements a. A is a complement of C, and m A = 47°. Find m C. 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°

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.

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.

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

• 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

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.

Example 4 Example: SOLUTION Use a Theorem

• Hw: Worksheet 2. 3 B • Quiz 2. 1 -2. 3 Friday