Name: __________________________________________________________
Date: ________________________________
Geometry
Ch. 3: Parallel & Perpendicular Lines
Investigate: Parallel Lines and Angles
Objective- To discover the relationships among the angles formed by two parallel lines and a transversal.
Directions- Use Geometer’s Sketchpad to construct two parallel lines cut by a transversal. Follow the
steps below to complete your construction and use your measurements to make conjectures regarding
the angles formed.
Part 1: Constructing Parallel Lines
Step 1: Use the straightedge tool to draw a line segment.
Step 2: Use the point tool to plot a point not on the line segment you just drew. Use the Label tool
to label the endpoints of your segment and the point not on the segment.
Step 3: Use the arrow to highlight segment AB and point C. From the Construct Menu, choose Parallel
Line. Use the Point tool to plot another point on the line you just created. Label the point D.
Step 4: Use the line tool to draw a line that intersects the parallel lines. Label the endpoints E and F.
Use the Arrow tool to highlight segment EF and segment AB. From the Construct Menu choose
Intersection. Label the new point G. Do the same for line CD and label the intersection H.
Part 2: Measurements
Step 1: Use the Arrow tool to highlight points (in this order!) A, G, and E. From the Measure Menu,
choose Angle. Record your measurements in the table below.
Step 2: Use the Arrow tool and Measure Menu to measure all angles listed in the table. The vertex
should be the 2nd letter highlighted for all angles!
Angle
Measure
<AGE
<EGB
<BGH
<AGH
<GHC
<GHD
<CHF
<DHF
Part 3: Drawing Conclusions
Step 1: Print out your diagram. Using 2 colored pencils, shade all angles that are the same
measurement the same color.
Extend:
1. From the Measure menu, choose calculate. Find the sum of angles below and complete the chart.
Angles
Sum
<BGH + <GHD
<AGH + <GHC
What do you notice about the sum of these angles?
Try it out:
1. If the lines in the diagram below are parallel, name 4 pairs of angles that will be congruent.
2. Name 2 pairs of angles that will be supplementary.