DATE PERIOD. Lesson Reading Guide. Line and Angle Relationships
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1 NAME DATE PERIOD Lesson Reading Guide Get Ready for the Lesson Read the introduction at the top of page 306 in your textbook. Write your answers below. 1. Suppose that the measure of angles 4 and 6 are each 60. Using angle relationships you have previously learned, or a protractor, find and record the measure of each numbered angle. Explain your reasoning. 2. Congruent angles are angles that have the same measure. How can you verify that the two angles are congruent? Lesson Supplementary angles form a straight line. What is the sum of supplementary angles? Read the Lesson 4. Match the model with its name. Remember What You Learned a. supplementary angles b. complementary angles c. vertical angles d. perpendicular lines e. parallel lines Fill in the blanks to answer questions 5 and Two angles are complementary if the sum of their measure is. 6. Two angles are supplementary if the sum of their measure is. Chapter 6 9 Course 3
2 NAME DATE PERIOD Study Guide and Intervention Angle Relationships Vertical Angles Complementary Angles Supplementary Angles m 1 m 3 m 2 m m 1 m 2 90 m 1 m Points, Lines, and Planes Parallel Lines Perpendicular Lines Transversal transversal Example Find the value of x. The angles are opposite each other and formed by intersecting lines, so they are vertical angles. Vertical angles are congruent. Exercises Find the value of x in each figure For Questions 5 and 6, use the figure at the right. 5. Find the measure of angle 2. Explain your reasoning Find the measure of angle 4. Explain your reasoning Chapter 6 10 Course 3
3 NAME DATE PERIOD Skills Practice Find the value of x in each figure Lesson For Exercises 13 and 14, use the figure at the right. 13. Find the measure of angle 2. Explain your reasoning. 14. Find the measure of angle 6. Explain your reasoning Angles Q and R and complementary. Find m R if m Q Find m J if m K 29 and J and K are supplementary. Chapter 6 11 Course 3
4 NAME DATE PERIOD Practice Find the value of x in each figure (x 12) 140 (x 47) 80 Use the figure at the right to answer Find the measure of angle 2. Explain your reasoning. 11. Find the measure of angle 3. Explain your reasoning. 12. Find the measure of angle 4. Explain your reasoning. 13. Find the measure of angle 6. Explain your reasoning. 8 (2x 10) The measures of angles A and B are equal and complementary. What is the measure of each angle? 15. ALGEBRA Angles G and H are complementary. If m G 3x 6 and m H 2x 11, what is the measure of each angle? Chapter 6 12 Course 3
5 NAME DATE PERIOD Word Problem Practice 1. SYMBOLS The symbol below is an equal sign with a slash through it. It is used to represent not equal to in math, as in 1 2. If m 1 108, classify the relationship between 1 and 2. Then find m 2. Explain your reasoning. 2. SCISSORS Arturo opened a pair of scissors so that the angle between the blades is 38. What is the angle between the handles? ? Lesson LEG LIFTS Kiara does leg lifts each morning. For each repetition she lifts her legs 35 degrees off the ground. What is the measure of the angle formed by her body and legs in this position? 5. ALGEBRA Angles Q and R are supplementary. If m Q 4x 9 and m R 8x 3, what is the measure of each angle? 4. ALGEBRA Angles A and B are complementary. If m A 3x 8 and m B 5x 10, what is the measure of each angle? 6. ART The drawing below shows the side view of a drawing easel. A If m A is 82, what is the measure of its supplementary angle? Chapter 6 13 Course 3
6 NAME DATE PERIOD Enrichment Lines and Angles in Space In a plane two lines are either parallel or intersecting. In space, there are three possibilities: parallel, intersecting, or skew. Imagine holding two yardsticks in the air and that the lines created by the sticks extend forever in both directions. You could hold the sticks so that the lines meet or do not meet. If the lines ever meet, they are intersecting. If they do not intersect, they are either parallel or skew. If they are oriented in the same direction, they are parallel. If lines do not intersect and are not parallel, they are skew. Imagine that the figure to the right is a cubic room with a floor, ceiling, and four walls. Each corner is labeled with a letter for reference. The line segments that form the edges of the room are each contained in a line. D H C G AB and HG are parallel. BC and HG are skew. AB and BC are intersecting. A E B F Refer to the figure above for Exercises Determine if the lines are parallel, intersecting, or skew. 1. CD and AB 3. FG and AB 5. CD and EH 7. EH and AE Find the measure of each angle. 2. CD and DH 4. EH and FG 6. GH and AD 8. CD and EF 9. DAB 10. AFB 11. CHE CHALLENGE Determine if the given lines would be parallel, intersecting, or skew. 12. CE and GA 13. GB and DE 14. FH and BD Chapter 6 14 Course 3
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