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Name _____________________
Polygon Investigations
Tech Tuesday
Properties of the Midsegment of a Trapezoid
Go to: http://www.keypress.com/x19429.xml (This is also hyperlinked from the weebly
site.)
Directions:
The midsegment of a trapezoid connects the midpoints of the two nonparallel sides of the
trapezoid. Use this web page to investigate the properties of the trapezoid midsegment.
The sketch on your screen shows trapezoid ARTE with midsegment MD and a copy,
A'R'T'E'. Drag any of the vertices of trapezoid ARTE to change the shape of both
trapezoids. You can move trapezoid A'R'T'E' by dragging point R'.
Investigate
1. Drag the copy A'R'T'E' onto trapezoid ARTE so that you can compare the
corresponding angles: Put angle TMD on top of angle TRA, then put angle EDM on
top of EAR.
What do you notice about these angles?
2. Fill in the blank from your notes: Trapezoid Midsegment Conjecture: The
midsegment of a trapezoid is ___________ to the bases and is equal in length to
________________.
3. Press Show Measurements to measure the two bases and the midsegment of
trapezoid ARTE. Make 3 different trapezoids and record your measurements here.
RA
MD
TE
Trapezoid 1
Trapezoid 2
Trapezoid 3
4. Prove this conjecture by SHOWING YOUR WORK to show that the midsegment is the
average of the 2 bases.
Properties of Parallelograms
Go to: http://www.keypress.com/x19430.xml (This is also hyperlinked from the weebly
site.)
Directions:
This sketch shows parallelogram LOVE and the measures of its angles. Drag vertices L, O,
or V to change the parallelogram. If you drag a point off the screen, press Start Over to
return it.
Investigate
1. Change the shape of the parallelogram and watch the measures of the pairs of
opposite angles.
a) What do you notice about angles LOV and VEL?
b) What do you notice about angles OVE and ELO?
2. Formulate the Parallelogram Opposite Angles Conjecture: The opposite angles of a
parallelogram are _____________.
Two angles that share a common side in a polygon are consecutive angles. For
example, in parallelogram LOVE, angles LOV and OVE are a pair of consecutive
angles.
3. Press Show Sums to see the sum of the measures of each pair of consecutive
angles. What do you notice about the sum of consecutive angles?
4. Formulate the Parallelogram Consecutive Angles Conjecture: The consecutive
angles of a parallelogram are _____________.
5. Describe how to use the two conjectures you just made to find all the angles of a
parallelogram with only one angle measure given.
If you finish early, go to: http://www.keypress.com/x19426.xml and try
some of the other investigations! These will give you some more visual
examples as to how these conjectures work.