Quadrilaterals Worksheet With Answers Page 14
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50We will investigate another property of parallelograms using the TI-83+ graphing
calculator with Cabri Junior ™ . This property involves the relationship between any two
consecutive angles of a parallelogram.
1. Make a conjecture about this relationship.
Conjecture:_____________________________________________________
Test this conjecture by measuring any two consecutive angles of a
parallelogram.
a) Begin with a parallelogram drawn on the viewing screen of a TI-83+
graphing calculator with Cabri Junior ™ or use
ABCD from the
previous investigation.
b) Measure two consecutive angles as shown in figure 4 below. These
measurements are for the parallelogram drawn.
figure 4
These results can be summarized in the following theorem for parallelograms.
Theorem
Any two consecutive angles of a parallelogram
are supplementary.
This proof follows from the definition of a parallelogram.
Proof:
In figure 4 above, we have ∠ A and ∠ B supplementary because AD
BC by
the definition of parallelogram. Using a similar argument, other pairs of
consecutive angles in the parallelogram can be shown supplementary.
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