6.3 Showing Quadrilaterals are Parallelograms

Bicycles
DERAILLEURS (named from
the French word meaning
“to derail”) move the chain
to change gears.
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Using Diagonals Tell whether the quadrilateral is a parallelogram.
Explain your reasoning.
17. 18. 19.
20. Bicycle Gears When you change
gears on a bicycle, the derailleur
moves the chain to the new gear.
For the derailleur at the right,
AB 1.8 cm, BC 3.6 cm,
CD 1.8 cm, and DA 3.6 cm.
Explain why AB&* and CD &** are always
parallel when the derailleur moves.
21. Error Analysis What is wrong with the student’s argument below?
A quadrilateral that has one pair
of sides congruent and the other
pair of sides parallel is always a
parallelogram.
You be the Judge
22. Three of the interior angles of a
quadrilateral have measures of 75, 75, and 105. Is this enough
information to conclude that the quadrilateral is a parallelogram?
Explain your answer.
23. Visualize It! Explain why the following method of drawing a
parallelogram works. State a theorem to support your answer.
●1 Use a ruler to draw ●2 Draw another ●3
a segment and its
midpoint.
segment so the
midpoints coincide.
6 4
7
5
B C
A D
Connect the
endpoints of the
segments.
24. Challenge If one pair of opposite sides of a quadrilateral is both
congruent and parallel, is the quadrilateral a parallelogram?
Explain your reasoning.
6.3 Showing Quadrilaterals are Parallelograms 321