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Transcript
Properties of Parallel Lines SketchPad In this investigation, you will discover relationships among the angles formed when parallel lines are cut by a transversal. Sketch and Investigate 1. Construct line AB and point C not on line AB. 2. Construct a line parallel to line AB, by highlighting the point and the line and choosing Parallel Line in the construct menu. Label a point on this new line C. 3. Construct line CA. Drag points C and A to make sure the three lines are attached at those points. 4. Use the Text tool to label points D, E, F, G and H as shown below. 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. Drag point A or B. Which angles stay congruent? Drag the transversal line CA (Do not change the point order on your lines) How many of the eight angles you measured appear to always be congruent? Adapted from activities from Key Curriculum Press 7. When two parallel lines are cut by a transversal, special angle pairs are formed. Study the chart below before filling in a second angle pair of each type; state what relationship, if any, you observe between the angles in each pair type . Angle Type Corresponding Alternate interior Alternate exterior Same-side interior angles Same-side exterior 8. Pair 1 Angle FCE CAB Angle ECA CAG Angle FCE HAG Angle ECA BAC Angle FCD HAG Pair 2 Relationship and Angle and Angle and Angle and Angle and Angle One of the angle types has four pair. In the chart below, name that angle type and name the third and fourth pairs of angles. Angle Type Pair 3 Pair 4 Relationship 9. We will now investigate the converses of your conjectures. In a new sketch, draw two lines that are not parallel. Adapted from activities from Key Curriculum Press 10. Use the previous diagram as a reference to add points as needed in order to measure the angles. Measure the eight angles formed by the three lines and record their measurements below. 11. Move the lines until you have two sets of four congruent angles. 12. What do you notice about the corresponding, alternate interior angles, and alternate exterior angles when the lines are not parallel? 13. What do you notice about the same side interior angles when the lines are not parallel? 14. 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 the lines are _______________. Geometry in the Trees Angles Unlimited 2 Properties of Parallel Lines (Suggested Answers) 5. (Answers will vary.) Adapted from activities from Key Curriculum Press 7. Angle Type Corresponding Alternate interior Alternate exterior Same-side interior angles Same-side exterior 8. Angle Type Corresponding Pair 1 Angle FCE CAB Angle ECA CAG Angle FCE HAG Angle ECA BAC Angle FCD 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 and Angle and Angle and Angle and Angle and Angle 14. Parallel. Adapted from activities from Key Curriculum Press Congruent Congruent Supplementary Supplementary
