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Honors Geometry

Honors Geometry. Today: Go over Quizzes 1.5 Instruction I will not be here tomorrow…. Bring compass and protractor to class on Friday. 1.5 Angle Relationships Objective: Identify and use special pairs of angles. Identify and use congruent angles and the bisector of an angle. Concept.

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Honors Geometry

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  1. Honors Geometry Today: • Go over Quizzes • 1.5 Instruction • I will not be here tomorrow…. • Bring compass and protractor to class on Friday.

  2. 1.5 Angle Relationships Objective: • Identify and use special pairs of angles. • Identify and use congruent angles and the bisector of an angle.

  3. Concept

  4. Concept

  5. Concept

  6. EXAMPLE 1 A. Name two adjacent angles whose sum is less than 90. Example 1a

  7. EXAMPLE 1 B. Name two acute vertical angles. Example 1b

  8. Concept

  9. Concept

  10. Concept

  11. If angles are vertical angles, then they are . • If two angles are complementary, then the sum of their measures is . • If two angles add up to , then they are complementary. • If two angles are supplementary, then the sum of their measures is . • If two angles add up to , then they are supplementary.

  12. EXAMPLE 2 ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle. Answer:mA = 31°, mB = 149° Example 2

  13. EXAMPLE 2 ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other. How does the problem Change???? Example 2

  14. EXAMPLE 2 The measure of an angle is ½ its supplement. What is the measure of the angle? 60° The measure of an angle is 25 less than 4 times its complement. What is the measure of the angle? 67°

  15. EXAMPLE 2 An angle’s supplement is 3 times larger than the angle. What is the measure of the angle? 45° An angle and its supplement are in the ratio of 11:7, what is the angle and its supplement? 110° and 70°

  16. EXAMPLE 2 If the measure of an angle is 8۩ – 5₪, what is its complement and supplement. 90 – 8۩ + 5₪ 180 – 8۩ + 5₪ If an angle’s supplement is 7 times larger than its complement, what is the angle? 75°

  17. Concept

  18. ALGEBRA Find x and y so thatKO and HM are perpendicular. EXAMPLE 3 Answer: x = 7 and y = 28 Example 3

  19. Assumptions

  20. EXAMPLE 4 A. Determine whether the following statement can be justified from the figure below. Explain. mVYT = 90 Example 4

  21. EXAMPLE 3 B. Determine whether the following statement can be justified from the figure below. Explain. TYW andTYU are supplementary. Answer: Yes, they form a linear pair of angles. Example 4

  22. EXAMPLE 3 C. Determine whether the following statement can be justified from the figure below. Explain. VYW andTYS are adjacent angles. Answer: No, they do not share a common side. Example 4

  23. Due Thursday: 1.5 P. 51-52 #9-17 odd ,21, 23, 29, 35, 49 1.5 MORE PRACTICE! Assignment

  24. What’s That Angle? You will be given the measure of an angle and asked to find either the complement or supplement. The winner moves on, the loser sits. First we practice. Complement of 15° Supplement of 25°

  25. Complement of 40° Supplement of 140° Complement of 10° Supplement of 50° Supplement of 172° Complement of 100° Complement of 32° Supplement of 136° Complement of 19° Complement of 17° Complement of 57°

  26. Complement of 37° Supplement of 125° Complement of 68° Supplement of 111° Supplement of 99° Complement of 1° Complement of 22° Supplement of 175° Complement of 4° Complement of 78° Complement of 33°

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