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Splash Screen. CCSS. Content Standards Preparation for G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Mathematical Practices 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. Then/Now.

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  1. Splash Screen

  2. CCSS Content Standards Preparation for G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Mathematical Practices 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others.

  3. Then/Now You measured and classified angles. • Identify and use special pairs of angles. • Identify perpendicular lines.

  4. Vocabulary • adjacent angles • linear pair • vertical angles • complementary angles • supplementary angles • perpendicular

  5. Vocabulary • Adjacent angles: • two angles that lie in the same plane and have a common vertex and a common side

  6. Vocabulary • Linear pair: • a pair of adjacent angles with noncommon sides that are opposite rays for a total measure of 180°

  7. Vocabulary • Vertical angles: • two nonadjacent angles formed by two intersecting lines that have equal measure

  8. Vocabulary • Complementary angles: • two angles with measures that have a sum of 90°

  9. Vocabulary • Supplementary angles: • two angles with measures that have a sum of 180°

  10. Vocabulary • Perpendicular: • lines, segments, or rays that form right angles

  11. Concept

  12. Identify Angle Pairs A. ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair.

  13. Identify Angle Pairs A. ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair. A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. Sample Answers:PIQ and QIS, PIT and TIS, QIU and UIT

  14. Identify Angle Pairs B. ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles.

  15. Identify Angle Pairs B. ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles. Sample Answers:PIU and RIS, PIQ and TIS, QIR and TIU

  16. Angle Measure 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.

  17. Angle Measure 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. UnderstandThe problem relates the measures of two supplementary angles. You know that the sum of the measures of supplementary angles is 180. Plan Draw two figures to represent the angles.

  18. Angle Measure Solve 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side. x = 31 Divide each side by 6.

  19. Angle Measure Use the value of x to find each angle measure. mA = x mB = 5x – 6 = 31 = 5(31) – 6 or 149 Check Add the angle measures to verify that the angles are supplementary. mA + mB = 180 31 + 149 = 180 180 = 180  Answer:mA = 31, mB = 149

  20. ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other.

  21. ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other. A. 1°, 1° B. 21°, 111° C. 16°, 74° D. 14°, 76°

  22. Concept

  23. Concept

  24. ALGEBRA Find x and y so thatKO and HM are perpendicular. Perpendicular Lines

  25. Interpret Figures A. Determine whether the following statement can be justified from the figure below. Explain. mVYT = 90

  26. Interpret Figures A. Determine whether the following statement can be justified from the figure below. Explain. mVYT = 90

  27. Interpret Figures B. Determine whether the following statement can be justified from the figure below. Explain. TYW andTYU are supplementary.

  28. Interpret Figures 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.

  29. Interpret Figures C. Determine whether the following statement can be justified from the figure below. Explain. VYW andTYS are adjacent angles.

  30. Interpret Figures 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.

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