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Lesson 1-5

Lesson 1-5. Angle Relationships. Lesson Outline. Five-Minute Check Then & Now and Objectives Vocabulary Key Concept Examples Lesson Checkpoints Summary and Homework. Then and Now. You measured and classified angles. Identify and use special pairs of angles

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Lesson 1-5

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  1. Lesson 1-5 Angle Relationships

  2. Lesson Outline • Five-Minute Check • Then & Now and Objectives • Vocabulary • Key Concept • Examples • Lesson Checkpoints • Summary and Homework

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

  4. Objectives • Identify and use special pairs of angles • Identify perpendicular lines

  5. Vocabulary • Adjacent angles – two coplanar angles that have a common vertex, a common side, but no common interior points • Linear pair – a pair of adjacent angles whose noncommon sides are opposite rays (always supplementary) • Vertical angles – two non adjacent angles formed by two intersecting lines Vertical angles are congruent (measures are equal)!! • Complementary Angles – two angles whose measures sum to 90° • Supplementary Angles – two angles whose measures sum to 180° • Perpendicular – two lines or rays are perpendicular if the angle (s) formed measure 90°

  6. Key Concept Looks like: • Y (on its side) • X

  7. Example 1A 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

  8. Example 1B 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

  9. Key Concept • m = m • Add to 90 • Add to 180

  10. 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. Let the measure of one angle be x. Solve Given 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side. x = 31 Divide each side by 6.

  11. Example 2 cont 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. Use the value of x to find each angle measure. mA = x mB = 5x – 6 = 31 = 5(31) – 6 or 149 CheckAdd 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

  12. Key Concept • perpendicular means right angle

  13. ALGEBRA Find x and y so thatKO and HM are perpendicular. Example 3 If KO HM, then mKJH = 90. To find x, use KJI and IJH

  14. Example 3 cont mKJH = mKJI + mIJH Sum of parts = whole 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. 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

  15. Key Concept • Be careful what you assume! • 89° and 91° may be hard to tell apart from 90°

  16. Example 4A Answer: Yes; VY and TX are perpendicular A. Determine whether the following statement can be justified from the figure below. Explain. mVYT = 90 The diagram is marked to show that VY  TX. From the definition of perpendicular, perpendicular lines intersect to form congruent adjacent angles.

  17. Example 4B 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.

  18. Example 4C 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.

  19. Lesson Checkpoints

  20. Summary & Homework • Summary: • There are many special pairs of angles such as adjacent angles, vertical angles, complementary angles, supplementary angles, and linear pairs. • Homework: • pg 50-3: 8-15, 19-22

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