Investigation: Properties of Parallel Lines In this investigation you'll discover relationships among the angles formed when parallel lines are intersected by a third line called a transversal....

Investigation: Properties of Parallel Lines In this investigation you'll discover relationships among the angles formed when parallel lines are intersected by a third line called a transversal. Sketch: Step 1: Construct AB and point C, not on AB. Step 2: Construct a line parallel to line AB, through C. D ? ? Select Cand AB, then Construct/Parallel Line. Step 3: Construct line CA and points D, E, F, G, and H as shown. G B H Step 4: Measure the eight angles in your figure. To measure ZFCE, click points F, C, and E (in that order) and select Measure/Angle. Investigate: Step 5: Drag point A or B and watch which angles stay congruent. (Be careful not to change the point order on your lines--that will change the angles Sketchpad measures!) Watch how the angle measures change. It may be helpful to use Number/Calculate to find the sum of angle pairs that you expect to be supplementary. 8) Fill in the chart with other angle pairs of that type and then state how the measures of the pairs of angles are related. Note: there are more than two pairs of one of these types. + Angle Type Pair 1 Pair 2 How are they related? (Supplementary or congruent?) Corresponding ZFCE and ZCAB Alternate Interior ZECA and ZCAG Alternate Exterior ZFCE and ZHAG Interior on same side of transversal ZECA and ZBAC Exterior on same side of transversal FCD and ZHAG 9) A Use the text feature in Geometer's Sketchpad to add text to your diagram and label one of the pairs of angles from the chart above. Include a screen shot of your diagram including the measures of the angles and the labels you added. 10) Write 2 of the 5 conjectures based on your observations in the chart. (Note: you started with parallel lines!) What about the converses of the two conjectures you listed in 10)? Remember that the converse of a conditional (if-then) statement has the hypothesis and conclusion reversed. 11) State the converse of both your two statements from 10). (Note: you must conclude with parallel lines in the converse!) Are they also true? (yes/no)