Geometry
8.5: Trapezoid Midsegment Theorem
Sketchpad Discovery
Name: __________________________________________________
Date: ___________________________________________________
Essential Question: What is the relationship between bases and midsegment of a trapezoid?
A midsegment in a trapezoid connects the midpoints of the two nonparallel sides. In this investigation you
will construct a trapezoid and discover some properties of the midsegment of a trapezoid.
Part 1: Construct a Trapezoid and Midsegment.
1. Use the segment tool to construct a segment. Label the endpoints A and B.
2. Use the point tool to construct point C not on AB.
3. Highlight point C and segment AB. From the
Construct Menu choose parallel line.
4. Use the point tool to create a second point on the line
you just created. Label the point D.
5. Create the legs of your trapezoid. Highlight point A
and point C. From the Construct menu, choose segment.
Do the same for points B and D.
6. Highlight line CD. From the Display Menu choose
Hide parallel line. Highlight points C and D, from the
Construct Menu choose segment..
7. Construct midpoints on the two legs of the
trapezoid. Highlight segment AC, from the Construct
Menu choose midsegment. Do the same for segment
BD. Label the midpoints as E and F. Highlight points E
and F, from the Construct Menu choose segment.
Part 2: Investigate and Draw Conclusions
1. Highlight segments AB, EF, and CD. From the Measure Menu choose length. Record the lengths in
the table below:
Segment
Length
2. Drag point B, so that AB is 14 and drag D so that CD is 10. What is the length of EF the
midsegment?
3. Drag point B so that AB is 6 and drag D so that CD is 10. What is the length of EF the
midsegment?
Make a conjecture: What is the relationship between the length of the midsegment and the lengths
of the bases of a trapezoid?
4. Highlight segments AB, CD and EF. From the Measure Menu choose slope. Record the slopes in
the table below.
Segment
Make a conjecture: What is the relationship between the
midsegment and bases of a trapezoid?
Part 3: Use what you learned to complete the exercises below.
Length