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ESSENTIAL QUESTION What are Complementary and Supplementary Angles?

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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ESSENTIAL QUESTION What are Complementary and Supplementary Angles?

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  1. Review:-Construction of Bisected Segment andBisected Angle USING:a)rulerb)compassc)blank sheets

  2. ESSENTIAL QUESTION What are Complementary and Supplementary Angles?

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

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

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

  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. c. b.

  8. 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.

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

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

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

  12. 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 and2are nonadjacent. 3 and4are adjacent. b.

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

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

  15. 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

  16. 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. 10  12;10and 12 are both complementary to 11, so10  12by the Congruent Complements Theorem. ANSWER

  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. 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?

  20. Example 4 Use a Theorem Example: SOLUTION

  21. Hw: Worksheet 2.3B Quiz 2.1-2.3 Friday

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