1. Classifying Quadrilaterals
On a Cartesian Plane

2. Classify Quadrilateral
We will be classifying five types of quadrilaterals
Rectangle
Square
Rhombus
Parallelogram
Trapezoid

3. Rectangles Opposite sides are congruent Distance Formula
Opposite sides are parallel
Slopes
Adjacent lines form right angles

4. Squares All sides are congruent Distance Formula
Opposite sides are parallel
Slope
Adjacent lines form right angles
Slopes

5. Rhombus All sides are congruent Distance Formula
Opposite sides are parallel
Slope

6. Parallelograms Opposite sides form parallel lines Slopes
Opposite sides are congruent
Distance Formula

7. Only one set of parallel lines
Trapezoid
Only one set of parallel lines
Slope

8. Practice

9. ABCD has vertices (8,9),(9,3),(2,5) and (1,11)
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 D A C B
Task 2

10. Justify It looks like a parallelogram
Part 1
That means distance formula Opposites are the Congruent (same/equal)
So, AB = CD and BC =DA

11. Slopes- Opposites are equal (same)
Justifying …
Part 2
Slopes- Opposites are equal (same)
AB = CD and BC = DA

12. 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.
Justify M N P
Justify O
Task 3

13. Justify a Rectangle 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

14. Justify a Rectangle
Part 1
Distance Formula: prove NM OP, MP NO

15. Justify a Rectangle Part 2
Prove: Opposite sides are Parallel; They have the same Slopes.

16. Justify a Rectangle Part 3
Prove adjacent lines form right angles; Show Perpendicular slopes
They are not perpendicular!
Quadrilateral MNOP is not a Rectangle !

17. Practice

18. Which quadrilateral is TOCS? Justify.
Task 4

19. Prove MATH is a trapezoid. Find the area and perimeter.
Task 5

20. Find the equation of a line that includes an altitude of parallelogram MATH.
Justify
Task 8

21. Say What!? Write the equation of a line perpendicular.
Let’s choose segment MH.
Let’s use point A

22. Altitude 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

23. 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?
Task 11

24. Thus ends the Quadrilateral portion of proving shapes are what they appear to be.