Parallel and Perpendicular Lines
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1 Practice A Parallel and Perpendicular Lines 1. Measure the formed by the transversal and the parallel lines. Which seem to be congruent? In the figure, line r line s. Find the measure of each angle In the figure, line m line n. Find the measure of each angle In the figure, line a line b. 14. Name all congruent to Name all congruent to Name three pairs of supplementary. 17. Which line is the transversal?
2 Practice B Parallel and Perpendicular Lines 1. Measure the formed by the transversal and the parallel lines. Which seem to be congruent? In the figure, line m line n. Find the measure of each angle. Justify your answer _ In the figure, line a line b. Find the measure of each angle. Justify your answer _ In the figure, line r line s. 14. Name all congruent to Which line is the transversal?
3 Practice C Parallel and Perpendicular Lines In the figure, line a line b. 1. Name all congruent to Name all congruent to Name three pairs of supplementary. 4. Which line is the transversal? 5. If m 7 is 131, what is the m 8? _ 6. If m 4 is 57, what is the m 5? 7. If m 3 is 127, what is the m 8? 8. If a transversal were drawn perpendicular to line a and line b, what would be the measure of the formed? Draw a diagram to illustrate each of the following. 9. line x line y line z 10. line r line s and 11. line a line b and and transversal k transversal m with transversal t with eight congruent 1 2 and 3 4
4 Parallel Lines Review for Mastery Parallel and Perpendicular Lines Perpendicular Lines Parallel lines never meet. When parallel lines are cut by a transversal, 8 are formed, 4 acute and 4 obtuse. The acute are all congruent. The obtuse are all congruent. Any acute angle is supplementary to any obtuse angle. Perpendicular lines form right. In each diagram, parallel lines are cut by a transversal. Name the that are congruent to the indicated angle The congruent The congruent The congruent to 1 are: to a are: to z are: In each diagram, parallel lines are cut by a transversal and the measure of one angle is given. Write the measures of the remaining on the diagram
5 Challenge Pairing Off When two parallel lines are cut by a transversal, eight are formed. Of these, four are between the parallel lines, interior. 1. In this diagram, name the four interior formed by the parallel lines and the transversal. 2. Think of the interior in pairs. Name the two pairs of interior that are on opposite sides of the transversal. 3. What is true about the measures of 3 and 5 in the diagram above? in the diagram at the right? Use a protractor to verify your conjecture. 4. What is true about the measures of 4 and 6 in the diagram above? in the diagram at the right? Use a protractor to verify your conjecture. 5. Interior that are on opposite sides of the transversal are called alternate interior. Draw a conclusion about the measures of alternate interior formed by parallel lines and a transversal. Use your observation about the measures of alternate interior of parallel lines to find the measure of x in each of these diagrams m x = m x = m x =
6 Problem Solving Parallel and Perpendicular Lines The figure shows the layout of parking spaces in a parking lot. AB CD EF 1. Name all congruent to Name all congruent to Name a pair of supplementary. 4. If m 1 = 75, find the measures of the other. 5. Name a pair of vertical. _ 6. If m 1 = 90, then GH is perpendicular to _ The figure shows a board that will be cut along parallel segments GB and CF. AD HE. Choose the letter for the best answer. 7. Find the measure of 1. A 45 C 60 B 120 D Find the measure of 2. F 30 H 60 G 120 J Find the measure of 4. F 45 H 60 G 120 J Find the measure of 6. F 30 H 60 G 120 J Find the measure of 3. A 30 C 60 B 120 D Find the measure of 5. A 30 C 60 B 120 D Find the measure of 7. A 45 C 60 B 120 D 90
7 Reading Strategies Understanding Symbols The symbol stands for parallel. Parallel lines are the same distance apart and never meet. The yard lines marked on a football field are similar to parallel line segments. Segment AB is parallel to segment CD. This can be written: AB CD. 1. Identify another pair of parallel line segments in the figure above. 2. Use the symbol to write how the line segments are related. The symbol stands for perpendicular. Perpendicular lines meet to form a square corner. A square in a corner is used as a symbol in a figure to show that lines are perpendicular. Use this figure for Exercises Segment QR is perpendicular to segment TR. Write this with symbols. 4. Identify two other line segments that are perpendicular to each other. 5. What symbol in the figure tells you that line segments are perpendicular to each other?
8 Puzzles, Twisters & Teasers Line Up! Decide whether the lettered lines in each figure are parallel or perpendicular. Each answer has a corresponding letter. Circle the letter above your answer. Use the letters to solve the riddle R J U E parallel perpendicular parallel perpendicular C T P C parallel perpendicular parallel perpendicular I R O N parallel perpendicular parallel perpendicular What do you call it when you ride your bike around and around the block? Y L G
9 Answers CODE Practice A and º º 4. 50º º 6. 50º º 8. 45º º º º º º 14. 3, 5, , 6, Possible answer: 1 + 8, 2 + 7, 3 + 6, or line c Practice B and º; 1 and the 142º angle are supplementary º; 2 and the 142º angle are vertical 4. 38º; 1 and 5 are corresponding º; 5 and 6 are supplementary º; 8 and the 142º angle are alternate exterior 7. 38º; 6 and 7 are supplementary 8. 43º; 6 and the 137º are supplementary and 6 and 2 are alternate interior º; 5 and the 137º angle are vertical º; 5 and 6 are supplementary º; 7 and the 137º angle are supplementary º; 4 and 6 are corresponding º; 3 and 5 are alternate interior 14. 4, 6, line t Practice C Possible answer: 1 + 8, 2 + 7, 3 + 6, or line c 5. 49º º 7. 53º 8. 90º 9. Possible answer: 10. Possible answer: 11. Possible answer: Review for Mastery
10 1. 3, 5, 7 2. c, e, g 3. y, t, r B 12. H 13. B Reading Strategies 1. Possible answer. EF is parallel to GH. 2. EF GH 3. QR TR Possible answer: QS ST 5. the square in the corner 6. Puzzles, Twisters & Teasers Challenge 1. 3, 4, 5, and 5; 4 and Alternate interior of parallel lines are equal in measure, or congruent º 7. 35º + 45º = 80º 8. 70º 30º = 40º Problem Solving 1. 3, 5, 7, , 6, 8, Possible answer: 1, 2 4. m 3 = m 5 = m 7 = m 9 = 75º, m 2 = m 4 = m 6 = m 8 = m 10 = 105º 5. Possible answer: 2, 8 P A N T S 6. Possible answer: AB, CD, EF 7. B 8. H 9. B 10. H
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