Lesson 5 Menu Warm-up Problems 1.Name the vertex of  3. 2.Name a point in the interior of  ACB. 3.Name the sides of  ABC. 4.Name the angles with vertex.

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Lesson 5 Menu Warm-up Problems 1.Name the vertex of  3. 2.Name a point in the interior of  ACB. 3.Name the sides of  ABC. 4.Name the angles with vertex B that appear to be acute. 5.If BD bisects  ABC, m  ABD = 2x + 3, and m  DBC = 3x – 13, find m  ABD.

Lesson 5 MI/Vocab adjacent angles vertical angles linear pair complementary angles supplementary angles perpendicular Identify and use special pairs of angles. Identify perpendicular lines.

Lesson 5 KC1

Lesson 5 Ex1 Identify Angle Pairs A. Name two angles that form a linear pair. A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.

Lesson 5 Ex1 Identify Angle Pairs B. Name two acute vertical angles. There are four acute angles shown. There is one pair of vertical angles.

Lesson 5 KC2

Lesson 5 KC3

Lesson 5 Ex2 Angle Measure ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the other angle. ExploreThe 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.

Lesson 5 Ex2 Angle Measure 6x – 6= 180Simplify. 6x= 186Add 6 to each side. x= 31Divide each side by 6. Solve

Lesson 5 Ex2 Angle Measure Use the value of x to find each angle measure. m  A = xm  = 5x – 6 m  A = 31m  = 5(31) – 6 or 149 Answer: 31, 149 ExamineAdd the angle measures to verify that the angles are supplementary. m  A + m  B= = = 180

Lesson 5 KC4

Lesson 5 Ex3 Perpendicular Lines

Lesson 5 Ex3 Perpendicular Lines 90= (3x + 6) + 9xSubstitution 90= 12x + 6Add. 84= 12xSubtract 6 from each side. 7= xDivide each side by 12. Answer: x = 7

Lesson 5 Ex4 A. Determine whether the following statement can be justified from the figure below. Explain. m  VYT = 90 Interpret Figures

Lesson 5 Ex4 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

Lesson 5 Ex4 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. Interpret Figures