SAVE SAVE SAVE Geometry/Trig Name: _____________________________ GSP Lab Pairs of Angles & Parallel Lines Date: ______________________________ Directions: Throughout this exploration, you will examine properties of parallel lines and the angles formed by two parallel lines and a transversal. 1 – Open a new GSP file. 2 – Save the file as LastNameFirstNameParallel (Example: SmithJohnParallel) in your I Drive. When you are completely finished with this exploration you will drop this into my folder for grading. Each step the starts with a * indicates that you should click in the white space before continuing to make sure nothing is selected. 3 – To draw a pair of parallel segments follow the steps below: (Try and make the segments further apart) a – Select the line segment tool and draw a line segment. Label the end points A (left) and B (right). To label a point, right click on the point and select Label Point. *b – Select the point tool and draw a point below the line segment. Label the point C. *c – Highlight point C and Segment AB. d – While they are both highlighted, go to the Construct Menu and select Parallel Line. *e – Create point D to the right of point C on the line that goes through point C. You will know that the point is ON the line if the line turns blue. *f – Select points C and D. g – Go to the Construct Menu and select Segment. *h – Select Line CD at a point not on Segment CD. i – Go to the Display Menu and select Hide Parallel Line. *j – If you have done this correctly you should now only see Segment AB and Segment CD. If you move any of the four points the segments should remain parallel. Raise your hand to get help if this is not the case. 4 – To draw a transversal, follow the steps below: * Select segment EF first THEN click on AB or CD *a – Select the line segment tool and draw a transversal that intersects the two parallel segments AB and CD. Label the end points E (top) and F (bottom). *b – Select Segment AB and Segment EF. Go to the Construct Menu, select Intersection. Label the intersection point G. *c – Select Segment CD and Segment EF. Go to the Construct Menu, select Intersection. Label the intersection point H. 5 – To measure all angles, follow the steps below: a – Measure each of the eight angles that you have create. To measure an angle, you must select the three points that would name the angle IN ORDER and then go to the Measure Menu and select Angle. For instance to find mÐAGE, make sure nothing is selected. Highlight the points A, then G, then E. Then go to the Measure Menu and select Angle. b – The measurements that are placed in the upper left hand corner can be moved. Click and drag each angle measurement and place it in its angle. SAVE SAVE SAVE

7. Use the GSP calculator to find the following: 6. Draw a sketch of what you currently see (include point labels and angle measures). 7. Use the GSP calculator to find the following: *Go to the Measure Menu and select Calculate. Click on one of the angles, click the plus size, and then click on the other angle. Press OK. mÐAGH + mÐCHG = ________ mÐAGE + mÐFHC = ________ 8. List any observations at this point(types of angles / what they sum to, etc.)… _______________________________________________________________________________________________________________________________________________________________________________________________________________________ 9. Using the new angle pair vocabulary that we discussed yesterday, name an example of each type of angle from the diagram above: Corresponding Angles – ____________________ Alternate Interior Angles – _________________ Alternate Exterior Angles – ________________ Same Side Interior Angles – _________________ Same Side Exterior Angles - _______________ 10. Slowly move point E and/or F. Observe what happens to your angle measurements. Explain what you notice below. 11. Based on the angle measurements, make a conjecture (hypothesis) about each pair of angles created by two parallel lines and a transversal: If lines are parallel, then corresponding angles are _____________________________________. If lines are parallel, then alternate interior angles are _________________________________. If lines are parallel, then alternate exterior angles are __________________________________. If lines are parallel, then same side interior angles are _________________________________. If lines are parallel, then same side exterior angles are _________________________________. 12. When you have finished, save your GSP file. Call me over to check it is complete. Then email me ONE file. Subject should be “Block 3” or “Block 4” depending on the class you are in. Inside the email please put each partners name.