Classifying Quadrilaterals
On a Cartesian Plane
Classify Quadrilateral
• We will be classifying five types of quadrilaterals
Rectangle
Square
Rhombus
Parallelogram
Trapezoid
Rectangles
Opposite sides are congruent
Distance Formula
Opposite sides are parallel
Slopes
Adjacent lines form right angles
Slopes
Squares
All sides are congruent
Distance Formula
Opposite sides are parallel
Slope
Adjacent lines form right angles
Slopes
Rhombus
All sides are congruent
Distance Formula
Opposite sides are parallel
Slope
Parallelograms
Opposite sides form parallel lines
Slopes
Opposite sides are congruent
Distance Formula
Trapezoid
Only one set of parallel lines
Slope
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 2
Slopes- Opposites are equal (same)
AB = CD and BC = DA
61
6
98
39
mAB
61
6
12
115
mCD
7
2
29
53
mBC
7
2
81
911
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 2
Prove: Opposite sides are Parallel; They have the same Slopes.
13
5
13
5
76
61
mMN
13
5
13
5
94
23
mOP
13
5, OPMNofSlopes
2
2
4
46
31
mNO 2
2
4
97
26
mMP
2, MPNOofSlopes
• Part 3 • Prove adjacent lines form right angles; Show
Perpendicular slopes
• They are not perpendicular!• Quadrilateral MNOP is not a Rectangle !
13
5, 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.