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Special Angle Pairs and Perpendicular Lines

Learn about special angle pairs and how to identify them in real-world examples. Understand the concept of perpendicular lines and how to interpret diagrams.

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Special Angle Pairs and Perpendicular Lines

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 1–4) 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 Lesson Menu

  3. A B C D Refer to the figure. Name the vertex of 3. A.A B.B C.C D.D 5-Minute Check 1

  4. A B C D Refer to the figure. Name a point in the interior of ACB. A.G B.D C.B D.A 5-Minute Check 2

  5. A B C D Refer to the figure. Which ray is a side of BAC? A.DB B.AC C.BD D.BC 5-Minute Check 3

  6. A B C D Refer to the figure. Name an angle with vertex B that appears to be acute. A. ABG B. ABC C. ADB D. BDC 5-Minute Check 4

  7. A B C D Refer to the figure. If bisects ABC, mABD = 2x + 3, andmDBC = 3x – 13, find mABD. A. 41 B. 35 C. 29 D. 23 5-Minute Check 5

  8. A B C D OP bisects MON and mMOP = 40°. Find the measure of MON. A. 20° B. 40° C. 60° D. 80° 5-Minute Check 6

  9. You measured and classified angles. (Lesson 1–4) • Identify and use special pairs of angles. • Identify perpendicular lines. Then/Now

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

  11. Concept

  12. 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 Example 1

  13. 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 Example 1

  14. A B C D 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 Example 1a

  15. A B C D B. Name two acute vertical angles. A.BAN and EAD B.BAD and BAN C.BAC and CAE D.FAN and DAC Example 1b

  16. Concept

  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. Example 2

  18. Angle Measure Solve 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side. x = 31 Divide each side by 6. Example 2

  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 Example 2

  20. A B C D 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° Example 2

  21. Concept

  22. ALGEBRA Find x and y so thatKO and HM are perpendicular. Perpendicular Lines Example 3

  23. 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. Example 3

  24. Perpendicular Lines To find y, use mMJO. mMJO = 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 Example 3

  25. A B C D A.x = 5 B.x = 10 C.x = 15 D.x = 20 Example 3

  26. Concept

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

  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. Example 4

  29. 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. Example 4

  30. A B A. Determine whether the statement mXAY = 90 can be assumed from the figure. A. yes B. no Example 4a

  31. A B B. Determine whether the statement TAU iscomplementarytoUAY can be assumed from the figure. A. yes B. no Example 4b

  32. A B C. Determine whether the statement UAX isadjacenttoUXA can be assumed from the figure. A. yes B. no Example 4c

  33. End of the Lesson

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