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Properties of Parallel Lines 2 In this investigation, you will discover relationships among the angles formed when parallel lines are cut by a transversal. Sketch and Investigate 1. In the space below, draw a line and label it AB. 2. Using both sides of a ruler, draw a line parallel to line AB and label a point on this new line C. 3. Draw line CA. 4. Label points D, E, F, G and H as shown below. Based on activities from Key Curriculum Press 5. Measure the eight angles in your figure and write their measurements below. Angle DCF _____ Angle FCE _____ Angle DCA _____ Angle ECA _____ Angle GAC _____ Angle CAB _____ Angle GAH _____ Angle HAB _____ 6. When two parallel lines are cut by a transversal, special angle pairs are formed. These special angle pairs have specific names and properties. The chart below shows one example of each type of angle pair. Fill in the chart with a second angle pair of each type, then state what relationship, if any, you observe between the angles in a pair type . Angle Type Corresponding Alternate interior Alternate exterior Same-side interior angles Same-side exterior 7. Pair 1 Angle FCE and Angle CAB Angle ECA and Angle CAG Angle FCE and Angle HAG Angle ECA and Angle BAC Angle FCD and Angle HAG Pair 2 Relationship One of the angle types has more four pair. Name that angle type in the chart below, and name the third and fourth pairs of angles of that type. Based on activities from Key Curriculum Press Angle Type Pair 3 Pair 4 Relationship 8. We will now investigate the converses of your conjectures. In the space below, draw two lines that are not parallel. Draw a transversal. 9. Add points as needed in order to measure all eight angles formed by the three lines. Record their measurements below. 10. What do you notice about the corresponding, alternate interior and alternate exterior angles when the lines are not parallel? 11. What do you notice about the same side interior angles when the lines are not parallel? Based on activities from Key Curriculum Press 12. Complete: If two lines are cut by a transversal so that corresponding angles, alternate interior angles, and alternate exterior angles are congruent, and same side interior angles are supplementary, then... Geometry in the Trees Angles Unlimited 2 Properties of Parallel Lines (suggested answers) 1. Based on activities from Key Curriculum Press 5. Measure the eight angles in your figure and write their measurements below. (Answers will vary.) 6. Angle Type Corresponding Alternate interior Alternate exterior Same-side interior angles Same-side exterior 7. Angle Type Corresponding Pair 1 Angle FCE and Angle CAB Angle ECA and Angle CAG Angle FCE and Angle HAG Angle ECA and Angle BAC Angle FCD and Angle HAG Pair 2 Angle FCD and Angle CAG Angle DCA and angle CAB Angle FCD and angle BAH Angle DCA and Angle CAG Angle FCE and Angle BAH Relationship Congruent Pair 3 Pair 4 Relationship Angle ECA and angle BAH Angle DCA and angle GAH Congruent Based on activities from Key Curriculum Press Congruent Congruent Supplementary Supplementary 8. 9. Add points as needed. Measure all eight angles formed by the three lines and record their measurements below. (Answers will vary) 10. What do you notice about the corresponding, alternate interior, and alternate exterior angles when the lines are not parallel? (They are not congruent) 11. What do you notice about the same side interior angles when the lines are not parallel? (They are not supplementary.) 12. The lines are parallel Based on activities from Key Curriculum Press
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