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.