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.