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Honors Geometry _________________________ Name Investigation with Parallel Lines and Associated Angles SKETCHPAD 1. Using Sketchpad, draw two lines which are not parallel, and draw a third line which crosses these two. (The third line is called a transversal.) 2. Construct enough points (8) to label all of the angles shown. (Note that your angles will not be called < 1,<2, <3, etc..) (Note: Use the point tool to place a point on the lines. Use the text tool to label the points. If the points are not labeled as above, you can double click on the label and a box will pop up and you can rename the points.) 3. Measure all 8 angles, and record your results below. 4. Record 3 sets of measurements. (Record a set, move one of the lines, record measurements again, move one line, and record the measurements again. m< 1 = m< 2 = m< 3 = m< 4 = m< 5 = m< 6 = m< 7 = m< 8 = 5. m< 1 = m< 2 = m< 3 = m< 4 = m< 5 = m< 6 = m< 7 = m< 8 = m< 1 = m< 2 = m< 3 = m< 4 = m< 5 = m< 6 = m< 7 = m< 8 = Save your Sketchpad document as NONPARALLEL. I may ask to see your document in class. Parallel/Non Parallel Lines & Angles Investigation page 2 6. Using Sketchpad, construct ABD first. Mark points A, B, and D on the line. Choose a point H which is not on AB , using the point tool. Construct segment CBHF (Highlight A and C, and construct a line.). By the way, I am following the drawing above. Choose H and ABD , and construct a line through H parallel to ABD . Construct other points in the drawing above. (You can extend the line segments, or you can make them into lines, if necessary, in order to name all angles with three letters, as Sketchpad requires you to do. You cannot use the numbered names for angles in Sketchpad. 7. Measure all of the angles three times, as you did in the investigation above. m< 1 = m< 2 = m< 3 = m< 4 = m< 5 = m< 6 = m< 7 = m< 8 = m< 1 = m< 2 = m< 3 = m< 4 = m< 5 = m< 6 = m< 7 = m< 8 = m< 1 = m< 2 = m< 3 = m< 4 = m< 5 = m< 6 = m< 7 = m< 8 = 8. Save your Sketchpad document as PARALLELS. 10. QUESTIONS: a) Are there any congruent angles? If so, which ones? b) Are there any supplementary angles? If so, which ones? c) Are there any complementary angles? If so, which ones? NEW DEFINITIONS. Parallel/Non Parallel Lines & Angles Investigation page 3 A transversal is a line which intersect two other lines. When a transversal intersects two lines, then four of the angles are on the “outside” of the two lines. They are called exterior angles. (In the drawing, < 1, <2, <7, and<8 are exterior angles.) When a transversal intersects two lines, then four of the angles are on the “inside” of the two lines. They are called interior angles. . (In the drawing, < 3, <4, <5, and<6 are exterior angles.) When a transversal intersects two lines, corresponding angles are a pair of angles so that one is an interior angle and the other is an exterior angle. They lie on the same side of the transversal. When a transversal intersects two lines, alternate interior angles are a pair of angles so that both are interior angles. They lie on the opposite side of the transversal. When a transversal intersects two lines, alternate exterior angles are a pair of angles so that both are exterior angles. They lie on the opposite side of the transversal. When a transversal intersects two lines, same side interior angles are a pair of angles so that both are interior angles. They lie on the same side of the transversal. When a transversal intersects two lines, same side exterior angles are a pair of angles so that both are exterior angles. They lie on the same side of the transversal. 11. Look at your two investigations above----one with non parallel lines cut by a transversal, and the other with parallel lines cut by a transversal. See if there are some conclusions that appear to be true (conjectures). Angles With non-parallel lines With parallel Lines ___________________________________________________________ corresponding alternate interior alternate exterior same-side interior same-side exterior Parallel/Non Parallel Lines & Angles Investigation 12. State these conjectures in the IF … THEN … format If lines are parallel and cut by a transversal, then corresponding angles are _________________. Add other similar statements…… page 4