6.6 Reasoning About
Special Quadrilaterals
Textbook page 337
What makes a quadrilateral a
parallelogram?
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Both pairs of opposite sides are parallel
OR both pairs of opposite sides are
congruent
OR all pairs of consecutive angles are
supplementary
OR both pairs of opposite angles are
congruent
OR the diagonals bisect each other
What makes a quadrilateral a
rhombus?
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is a parallelogram
AND all sides are congruent
What makes a quadrilateral a
rectangle?
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is a parallelogram
AND has four congruent angles (900
each)
What makes a quadrilateral a
square?
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is a parallelogram
AND has four congruent sides
AND has four congruent angles (900
each)
What makes a quadrilateral a
trapezoid?
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EXACTLY ONE pair of parallel sides
What makes a quadrilateral an
isosceles trapezoid?
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is a trapezoid
AND has congruent legs
Quadrilaterals
parallelogram
ordinary
parallelogram
trapezoid
rhombus
ordinary
rhombus
rectangle
square
ordinary
rectangle
ordinary
trapezoid
ordinary
quadrilateral
isosceles
trapezoid
Examples on pg 338
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1) no, all four angles are 900 so it is a rectangle, but
there is no information about the sides, so you cannot
conclude that PQRS is a square
2) no, both pairs of opposite angles are congruent, so
the figure is a parallelogram, but there is no information
about the sides, so you cannot conclude that WXYZ is a
rhombus
3) yes, <L and <M are supplementary so KL and JM are
parallel by same side interior angles converse, Since <J
and <M are not supplemntary, KJ is not parallel to LM.
The figure has exactly one pair of parallel sides, so it is a
trapezoid.
Homework
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Assignment # 15
Pg 339
Problems 1-23 all, 26, 27-37 odd
Do not pack up before you are finished
or you are told to do so by Mrs.
Takayama