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Review: -Construction of Bisected Segment and Bisected Angle USING: a)ruler b)compass c)blank sheets. ESSENTIAL QUESTION What are Complementary and Supplementary Angles?. Complementary Angles: two angles whose measure is 90 °. Vocabulary.
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Review:-Construction of Bisected Segment andBisected Angle USING:a)rulerb)compassc)blank sheets
ESSENTIAL QUESTION What are Complementary and Supplementary Angles?
Complementary Angles: two angles whose measure is 90° Vocabulary
Supplementary Angles: two angles whose measure is 180° VOCABULARY
Example 1 Identify Complements and Supplements Determine whether the angles are complementary, supplementary,or neither. a. c. b.
Example 1 SOLUTION Identify Complements and Supplements Determine whether the angles are complementary, supplementary,or neither. c. a. b. a. supplementary. complementary nor supplementary. b. complementary. c.
Checkpoint Identify Complements and Supplements Determine whether the angles are complementary, supplementary,or neither. 1. 2. 3.
Checkpoint ANSWER ANSWER ANSWER supplementary complementary neither Identify Complements and Supplements Determine whether the angles are complementary, supplementary,or neither. 1. 2. 3.
Adjacent Angles: two angles that share a common vertex and a common side (ray).
Example 2 SOLUTION c. Although 5 and 6 share a common vertex, they do not share a common side. Therefore, 5 and 6 are nonadjacent. Identify Adjacent Angles Tell whether the numbered angles are adjacent or nonadjacent. b. c. a. a. 1 and2are nonadjacent. 3 and4are adjacent. b.
Complements: their sum = 90° Supplements: their sum = 180°
Example 3 SOLUTION a. Measures of Complements and Supplements a. A is a complement of C, and mA=47°. Find mC. P is a supplementof R, and mR=36°. Find mP. b. b. mA+mC=90° mP+mR=180° 47°+mC =90° mP+36°=180° 47°+ mC– 47°=90° – 47° mP +36°– 36°=180° – 36° mP = 144° mC = 43°
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. Vocabulary
Checkpoint Use a Theorem In the diagram,m10 + m11 = 90°, and m11 + m12 = 90°. Name a pair of congruent angles. Explain your reasoning. 10 12;10and 12 are both complementary to 11, so10 12by the Congruent Complements Theorem. ANSWER
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 SOLUTION 7 and 9are both supplementary to 8. So, by the Congruent supplementsTheorem, 7 9. Use a Theorem 7 and 8are supplementary, and 8 and 9are supplementary. Are angles 8 & 9 congruent?
Example 4 Use a Theorem Example: SOLUTION
Hw: Worksheet 2.3B Quiz 2.1-2.3 Friday