1. My Favorite No!! D
EB = 7
AE = 10
DE = DC
Find AD E C B A

2. Chapter 4 Quadrilaterals

3. Quadrilateral

4. Parallelogram

5. Objectives
To identify any quadrilateral, by name, as specifically as you can, based on its characteristics
To use characteristics of quadrilaterals to solve for sides and/or angles
To write proofs involving all types of quadrilaterals.

6. Special Quadrilaterals
There are several special types of quadrilaterals.
They are classified based on their sides or angles.

7. Quadrilateral Family Tree
Kite
Right Trapezoid

8. A quadrilateral is a polygon with 4 sides.
Quadrilateral Family Tree
Right Trapezoid

9. Quadrilateral
a quadrilateral is a polygon with 4 sides.

10. Right Trapezoid

11. A parallelogram is a quadrilateral with two pairs of parallel sides.

12. Parallelogram
Definition: a quadrilateral with two pairs of parallel sides

13. Parallelogram:
A diagonal of a parallelogram separates it into two congruent triangles

14. Parallelogram:
The opposite angles of a parallelogram are congruent.

15. Parallelogram:
Two consecutive angles of a parallelogram are supplementary. 1 2

16. Parallelogram:
The opposite sides of a parallelogram are congruent.

17. Parallelogram:
The diagonals of a parallelogram bisect each other.

18. Parallelogram:
In a parallelogram with unequal pairs of consecutive angles, the longer diagonal lies opposite the obtuse angle.

19. Parallelogram: 5 ways showing a Quadrilateral is a Parallelogram:
Both pairs of opposite sides are parallel
If both pairs of opposites sides are congruent
If one pair of opposites sides are both parallel and congruent
If the diagonals bisect each other
If both pairs of opposite angles are congruent.

20. Parallelogram:

21. Parallelogram:

23. Kite
A kite is a quadrilateral with NO parallel sides but 2 pairs of adjacent congruent sides.

24. (adjacent congruent sides)
Definition: A kite is a quadrilateral with 2 pairs of consecutive congruent sides
(adjacent congruent sides)
Kite
2 in.
4 in.
No sides are parallel!

25. Kite
One pair of opposite sides are congruent.

26. Kite

27. Something else you need to know:
The line segment that joins the midpoint of two sides of a triangle has a length equal to one-half the length of the third side.

28. Try one:
If AB = 12.7
Find ED

29. Maybe two:
If DE = 2x + 1
AB = 5x - 1
Find: x, DE
and AB

30. EXIT TICKET!!!

31. Right Trapezoid

32. A rectangle is a parallelogram that is equiangular.

33. Rectangle
Definition: a parallelogram with 4 congruent angles, all 90 degrees.

34. Rectangle
Characteristics: 1) The diagonals are congruent

35. Rectangle
AC = 17
BC = 15
Find AB
Find BD A B D C

36. Rectangle

37. Rectangle

38. Right Trapezoid

39. A square is a specific case of both a rhombus AND a rectangle, equiangular and equilateral.

40. Square Definition: a regular parallelogram An equilateral rectangle
An equiangular rhombus

42. A rhombus is a parallelogram that is equilateral.

43. Rhombus
Definition: a parallelogram with 4 congruent sides.
4 in.
4 in.
4 in.
4 in.

44. Rhombus
Characteristics: 1) The diagonals of a rhombus are perpendicular.
4 in.
4 in.
4 in.
4 in.

45. Rhombus

46. A trapezoid is a quadrilateral with only one pair of parallel sides.
Right Trapezoid

47. A trapezoid is a quadrilateral with only one pair of parallel sides.

48. Trapezoid
Definition: a quadrilateral with exactly one pair of parallel sides.
trapezoids

49. An isosceles trapezoid is a trapezoid with the legs congruent.
Right Trapezoid
An isosceles trapezoid is a trapezoid with the legs congruent.

50. A right trapezoid has one leg ┴ to the // lines
An isosceles trapezoid is a trapezoid with the legs congruent.

51. Isosceles Trapezoid: a trapezoid with congruent legs.
Right Trapezoid
A trapezoid with parallel sides perpendicular to one leg.
a trapezoid with congruent legs.
Legs are the non-parallel sides