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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.

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

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Vocabulary adjacent angles linear pair vertical angles complementary angles supplementary angles perpendicular

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

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

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Vocabulary Vertical angles: two nonadjacent angles formed by two intersecting linesthat have equal measure

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

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

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

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Concept

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

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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

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

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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

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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.

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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. PlanDraw two figures to represent the angles.

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

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

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

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

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Concept

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Perpendicular Lines ALGEBRA Find x and y so that KO and HM are perpendicular.

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

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

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

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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.

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

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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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