Download - Classifying Quadrilaterals
Classifying QuadrilateralsOn a Cartesian Plane
Classify Quadrilateral
• We will be classifying five types of quadrilaterals
RectangleSquare
RhombusParallelogram
Trapezoid
Rectangles
Opposite sides are congruentDistance Formula
Opposite sides are parallelSlopes
Adjacent lines form right anglesSlopes
Squares
All sides are congruentDistance Formula
Opposite sides are parallelSlope
Adjacent lines form right anglesSlopes
Rhombus
All sides are congruentDistance Formula
Opposite sides are parallelSlope
Parallelograms
Opposite sides form parallel linesSlopes
Opposite sides are congruentDistance Formula
Trapezoid
Only one set of parallel linesSlope
Practice
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
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
Justifying …
Part 2Slopes- Opposites are equal (same)
AB = CD and BC = DA
616
9839
mAB
616
12115
mCD
72
2953
mBC
72
81911
mDA
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.
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
• Part 1• Distance Formula: prove NM OP, MP NO
1942394 22 OP 1946176 22 NM
194OPNM
202697 22 MP 203146 22 NO
20NOMP
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
• 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
Which quadrilateral is TOCS? Justify.
Prove MATH is a trapezoid. Find the area and perimeter.
Find the equation of a line that includes an altitude of parallelogram MATH.
Say What!?• Write the equation
of a line perpendicular.
• Let’s choose segment MH.
• Let’s use point A
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
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?
Thus ends the Quadrilateral portion of proving shapes are what they appear
to be.