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

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Presentation transcript:

Splash Screen

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

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

Concept

Example 1 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 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.A B.B C.C D.D Example 1a A.  CAD and  DAE B.  FAE and  FAN C.  CAB and  NAB D.  BAD and  DAC A. Name two adjacent angles whose sum is less than 90.

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

Concept

Example 2 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.

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

Example 2 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 

A.A B.B C.C D.D Example 2 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.

Concept

Example 3 Perpendicular Lines ALGEBRA Find x and y so that KO and HM are perpendicular.

Example 3 Perpendicular Lines 90= (3x + 6) + 9xSubstitution 90= 12x + 6Combine like terms. 84= 12xSubtract 6 from each side. 7= xDivide each side by 12.

Example 3 Perpendicular Lines To find y, use m  MJO. m  MJO =3y + 6Given 90 =3y + 6 Substitution 84= 3ySubtract 6 from each side. 28= yDivide each side by 3. Answer: x = 7 and y = 28

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

Concept

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

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

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

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