Transcript Angle Pairs
Five-Minute Check (over Lesson 1–4) CCSS Then/Now New Vocabulary Key Concept: Special Angle Pairs Example 1: Real-World Example: Identify Angle Pairs Key Concept: Angle Pair Relationships Example 2: Angle Measure Key Concept: Perpendicular Lines Example 3: Perpendicular Lines Key Concept: Interpreting Diagrams Example 4: Interpret Figures Over Lesson 1–4 Refer to the figure. Name the vertex of 3. A. A B. B C. C D. D Over Lesson 1–4 Refer to the figure. Name a point in the interior of ACB. A. G B. D C. B D. A Over Lesson 1–4 Refer to the figure. Which ray is a side of BAC? A. DB B. AC C. BD D. BC Over Lesson 1–4 Refer to the figure. Name an angle with vertex B that appears to be acute. A. ABG B. ABC C. ADB D. BDC Over Lesson 1–4 Refer to the figure. If bisects ABC, mABD = 2x + 3, and mDBC = 3x – 13, find mABD. A. 41 B. 35 C. 29 D. 23 Over Lesson 1–4 OP bisects MON and mMOP = 40°. Find the measure of MON. A. 20° B. 40° C. 60° D. 80° 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. You measured and classified angles. • Identify and use special pairs of angles. • Identify perpendicular lines. • adjacent angles • linear pair • vertical angles • complementary angles • supplementary angles • perpendicular Answer the questions using the diagram. Are 2 and 3 a linear pair? 1 2 4 3 SOLUTION No. The angles are adjacent but their noncommon sides are not opposite rays. 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 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 A. Name two adjacent angles whose sum is less than 90. A. CAD and DAE B. FAE and FAN C. CAB and NAB D. BAD and DAC B. Name two acute vertical angles. A. BAN and EAD B. BAD and BAN C. BAC and CAE D. FAN and DAC 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. Understand The 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. Angle Measure Solve 6x – 6 = 180 6x = 186 x = 31 Simplify. Add 6 to each side. Divide each side by 6. Angle Measure Use the value of x to find each angle measure. mA = x = 31 Check mB = 5x – 6 = 5(31) – 6 or 149 Add the angle measures to verify that the angles are supplementary. mA + mB = 180 31 + 149 = 180 180 = 180 Answer: mA = 31, mB = 149 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° W and Z are complementary. The measure of Z is 5 times the measure of W. Find m W SOLUTION Because the angles are complementary, m W + m Z = 90˚. But m Z = 5( m W ), so m W + 5( m W) = 90˚. Because 6(m W) = 90˚, you know that m W = 15˚. Perpendicular Lines ALGEBRA Find x and y so that KO and HM are perpendicular. Perpendicular Lines 90 = (3x + 6) + 9x Substitution 90 = 12x + 6 Combine like terms. 84 = 12x Subtract 6 from each side. 7 =x Divide each side by 12. Perpendicular Lines To find y, use mMJO. mMJO = 3y + 6 Given 90 = 3y + 6 Substitution 84 = 3y Subtract 6 from each side. 28 = y Divide each side by 3. Answer: x = 7 and y = 28 A. x = 5 B. x = 10 C. x = 15 D. x = 20 Interpret Figures A. Determine whether the following statement can be justified from the figure below. Explain. mVYT = 90 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. 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. A. Determine whether the statement mXAY = 90 can be assumed from the figure. A. yes B. no B. Determine whether the statement TAU is complementary to UAY can be assumed from the figure. A. yes B. no C. Determine whether the statement UAX is adjacent to UXA can be assumed from the figure. A. yes B. no