1. Homework: Quadrilaterals & Coordinate Geometry Day 1 Wkst
BIG QUIZ on Friday
Warm-Up: Draw a picture of each of the following and write down as much as you can remember
Trapezoid
Parallelogram
Rectangle
Square
Rhombus
Kite

2. Properties of Quadrilaterals
Trapezoid
Kite
Parallelogram
Names
Rhombus
Rectangle
Square

3. Sides Parallel Sides Trapezoid Kite 1 pair of parallel sides
Parallelogram
Rectangle
Square
Rhombus
Kite
1 pair of parallel sides
Sides
NO parallel sides
2 pairs of parallel sides
Parallel
Sides
2 pairs of parallel sides
2 pairs of parallel sides.
2 pairs of parallel sides

4. Sides Congruent Sides Trapezoid Kite 2 pair of adjacent sides are 
Parallelogram
Rectangle
Square
Rhombus
Kite
Sides
2 pair of adjacent sides are 
2 pair of opposite sides are 
Congruent
Sides
AL L sides 
2 pair of opposite sides are 
AL L sides 

5. Angles Angles Trapezoid Kite One opposite pair of equal angles
Parallelogram
Rectangle
Square
Rhombus
Kite
Opposite angles are equal.
One opposite pair of equal angles
Angles
Angles
Opposite angles are equal.
All angles are right angles (90o)
All angles are right angles (90o)

6. Diagonals Diagonals Trapezoid Kite Parallelogram Rhombus Rectangle
Square
Rhombus
Kite
Both diagonals bisect each other
One diagonal is bisected & are perpendicular
Diagonals
Diagonals
Both diagonals bisect each other & are 
Both diagonals bisect
Diagonals are perpendicular
Both diagonals bisect & are perpendicular

7. Sides, angles and diagonals
Trapezoid
Parallelogram
Rectangle
Square
Rhombus
Kite
Sides, angles and diagonals
All Three

8. Quadrilaterals – DRAW THIS
Kite
Parallelogram
Trapezoid
Rectangle
Rhombus
Isosceles
Trapezoid
Square

9. Classifying Quadrilaterals
Judging by appearance, classify each quadrilateral in as many ways as possible:
Square
Rectangle
Rhombus
Parallelogram
Quadrilateral
Parallelogram
Quadrilateral

10. Classifying Quadrilaterals
Judging by appearance, classify each quadrilateral in as many ways as possible:
Rhombus
Parallelogram
Quadrilateral
Trapezoid
Quadrilateral

11. Classifying Quadrilaterals
Judging by appearance, classify each quadrilateral in as many ways as possible:
Kite
Quadrilateral
Rectangle
Parallelogram
Quadrilateral

12. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(3, –2), B(2, –1), C(4, 3), D(5, 2)
Length of the four sides:
AB =
CD =
BC =
DA =

13. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(3, –2), B(2, –1), C(4, 3), D(5, 2)
Slope of the four sides:
AB =
CD =
BC =
DA =
Are the sides perpendicular? (Hint: look at the slopes)

14. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(3, –2), B(2, –1), C(4, 3), D(5, 2)
Slope of the Diagonals:
AC =
BD =
Are they perpendicular?

15. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(3, –2), B(2, –1), C(4, 3), D(5, 2)
Length of the Diagonals:
AC =
BD =
Point of intersection of the diagonals
(Point E)

16. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(3, –2), B(2, –1), C(4, 3), D(5, 2)
Length of the diagonal segments:
AE =
BE =
EC =
ED =

17. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(3, –2), B(2, –1), C(4, 3), D(5, 2)
CD || BA and BC || AD
parallelogram

18. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)
Length of the four sides:
AB =
CD =
BC =
DA =

19. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)
Slope of the four sides:
AB =
CD =
BC =
DA =
Are the sides perpendicular? (Hint: look at the slopes)

20. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)
Slope of the Diagonals:
AC =
BD =
Are they perpendicular?

21. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)
Length of the Diagonals:
AC =
BD =
Point of intersection of the diagonals
(Point E)

22. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)
Length of the Diagonals:
AC =
BD =
Point of intersection of the diagonals
(Point E)

23. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)
Length of the diagonal segments:
AE =
BE =
EC =
ED =

24. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
B. A(–3, 1), B(–4, 2), C(–3, 3), D(–2, 2)
TU || SR and ST || RU
TU^RU, RU^RS, RS^ST and ST^TU
parallelogram, rectangle, rhombus, square

25. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)
Length of the four sides:
AB =
CD =
BC =
DA =

26. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)
Slope of the four sides:
AB =
CD =
BC =
DA =
Are the sides perpendicular? (Hint: look at the slopes)

27. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)
Slope of the Diagonals:
AC =
BD =
Are they perpendicular?

28. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)
Length of the Diagonals:
AC =
BD =
Point of intersection of the diagonals
(Point E)

29. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)
Length of the diagonal segments:
AE =
BE =
EC =
ED =

30. Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
C. A(1, –1), B(1, –2), C(3, –3), D(3, 1)
GH || JI
trapezoid

32. Coordinate Geometry
Show that A(2, -1),
B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram.

33. Prove that there are 2 pairs of parallel sides
Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram.
Prove that there are 2 pairs of parallel sides
Slope of AB.
3-(-1) = - 4
1 - 2
Slope of CD.
1 – 5 = - 4
7 – 6
Slope of BC.
5 – 3 = 2
Slope of DA.
- 1 – 1 = 2

34. Prove that both pairs of opposite sides are congruent
Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram.
Prove that both pairs of opposite sides are congruent
AB=√(1 – 2)2 + [3 – (- 1)2] = √17
CD=√(7 – 6)2 + (1 - 5)2 = √17
BC=√(6 – 1)2 + (5 - 3)2 = √29
DA= √(2 – 7)2 + (-1 - 1)2 = √29

35. Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram.
Prove that the diagonals bisect each other.