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Geometer’s Sketchpad Activities Exploring Geometry Parallel Lines When two lines intersect they form four angles. The point of intersection of the lines is the vertex of all four angles. In this activity, you’ll investigate relationships between pairs of these angles. Sketch and Investigate You'll learn how to construct parallel lines and discover some important relationships with an intersecting third line called a transversal. 1. Construct a line AB and a point C, not on the line. B A C To construct a parallel line, select the line AB, hold the shift key down and select point C as well. Then, in the Construct menu choose parallel line 2. Construct a line parallel to AB through point C. Construct/label the second point on this parallel line. Label it point D. This makes lines AB & CD parallel (AB||CD). 3. Construct line CA. This line is called a transversal. Drag points C and A to make sure that all three lines are connected at those points. B A C D 4. Construct points D, E, F, G and H as shown in the picture. F B A E D C G H 5. Use Sketchpad to measure the eight angles that are formed in your figure. Be sure to be very systematic about your measuring so that you don't measure the same angle twice. 6. Drag point A or B and see what happens to the angles. Also drag the transversal CA. (Becareful not to drag the points and change the order on your lines. That would change some angles into other angles.) Make and record some of your observations. 582760082, Created by S. Middleton 1 revised: 05/06/17 7. When two parallel lines are crossed by a transversal, several pairs of angles are formed (think back to FiVZiX OIL). These pairs of angles have specific names. Each name is based upon the location of the angles in regards to which side of the transversal they are located on (SAME or ALTERNATE) and based upon whether they are on the INTERIOR or EXTERIOR of the parallel lines. 8. Complete the table below by first labeling the second pair of each type of angle. Every "type" of angle has at least two pairs, but only one of the types has 4 pairs, see if you can determine which type it is. (hint: Flip, turn, or rotate the letters from FiVZiX OIL to determine other pairs). sg Things to Do . . . To measure an angle, select three points. Make sure that you select the point you want to be the vertex in the middle of your selection. Then in MEASURE menu, choose ANGLE. Use GSP to measure the distance from point D to each of the angle’s sides and the angles that are formed. Measure the Corresponding Angles EAF & DCA and record them in the table below: Measure the Alternate Interior Angles EAC & GCA and record them in the table below: Measure the SAME-Side Interior Angles EAF & DCA and record them in the table below: Find a second pair of each type of angle and repeat the process. Type of Angles Pair 1 Corresponding EAF & DCA Alternate Interior EAC & GCA Same-side Interior DCA & EAC Measurements Pair 2 Measurements Points to Ponder Drag point F, H, D, or E to change the angles. How do the measures of the angles compare? Write a conjecture, about the measures of the Corresponding Angles formed by a transversal cutting across two parallel lines: Repeat the process of dragging points F, H, D or E. Write a conjecture, about the measures of the Alternate Interior Angles formed by a transversal cutting across two parallel lines: 582760082, Created by S. Middleton 2 revised: 05/06/17