Classifying Quadrilaterals
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Transcript of Classifying Quadrilaterals
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Classifying QuadrilateralsOn a Cartesian Plane
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Classify Quadrilateral
• We will be classifying five types of quadrilaterals
RectangleSquare
RhombusParallelogram
Trapezoid
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Rectangles
Opposite sides are congruentDistance Formula
Opposite sides are parallelSlopes
Adjacent lines form right anglesSlopes
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Squares
All sides are congruentDistance Formula
Opposite sides are parallelSlope
Adjacent lines form right anglesSlopes
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Rhombus
All sides are congruentDistance Formula
Opposite sides are parallelSlope
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Parallelograms
Opposite sides form parallel linesSlopes
Opposite sides are congruentDistance Formula
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Trapezoid
Only one set of parallel linesSlope
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Practice
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ABCD has vertices (8,9),(9,3),(2,5) and (1,11). What type of quadrilateral is ABCD? Justify. Find the perimeter and area of ABCD
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JustifyIt looks like a parallelogram
Part 1That means distance formula Opposites are the
Congruent (same/equal)So, AB = CD and BC =DA
373998 22 AB 373998 22 AB 3711512 22 CD
535329 22 BC 5311918 22 AD
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Justifying …
Part 2Slopes- Opposites are equal (same)
AB = CD and BC = DA
616
9839
mAB
616
12115
mCD
72
2953
mBC
72
81911
mDA
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If the coordinates of MNOP are M(7,6),N(-6,1),O(-4,-3) and P(9,2), what type of quadrilateral is MNOP?
Find the area and perimeter of MNOP.
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It appears to be a rectangle Need to show:
Opposite sides are congruent Distance Formula
Opposite sides are parallel Slopes are equal
Adjacent lines form right angles Perpendicular Slopes
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• Part 1• Distance Formula: prove NM OP, MP NO
1942394 22 OP 1946176 22 NM
194OPNM
202697 22 MP 203146 22 NO
20NOMP
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Part 2Prove: Opposite sides are Parallel; They have the
same Slopes.
13
5135
7661
mMN
135
135
9423
mOP
135, OPMNofSlopes
2
24
4631
mNO
224
9726
mMP
2, MPNOofSlopes
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• Part 3 • Prove adjacent lines form right angles; Show
Perpendicular slopes
• They are not perpendicular!• Quadrilateral MNOP is not a Rectangle !
135, OPMNofSlopes
2, MPNOofSlopes
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Which quadrilateral is TOCS? Justify.
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Prove MATH is a trapezoid. Find the area and perimeter.
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Find the equation of a line that includes an altitude of parallelogram MATH.
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Say What!?• Write the equation
of a line perpendicular.
• Let’s choose segment MH.
• Let’s use point A
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Steps:• Find the slope of the segment • Write the perpendicular slope• Use coordinate A• I suggest point slope formula• Simplify it into slope intercept
form
MH
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Connect the midpoints of the sides of ABCD consecutively to form a new quadrilateral. Which special quadrilateral is it? Justify. How large are the perimeter and area of the new figure in comparison to the same measures for ABCD?
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Thus ends the Quadrilateral portion of proving shapes are what they appear
to be.