1. Please click the speaker symbol on the left to hear the audio that accompanies some of the slides in this presentation.
Quadrilaterals

2. Quadrilateral: A Polygon with 4 sides and 4 angles
Quadrilateral: A Polygon with 4 sides and 4 angles. Sides: May or may not be congruent. Angles: The sum of all interior angles in a quadrilateral is 360o. Quad means “4” and lateral means “sides”.

3. Types of Quadrilaterals

4. In General …`
Quadrilaterals are polygons that have 4 sides and 4 angles.

5. Parallelograms
A parallelogram has two parallel pairs of opposite sides.

6. Parallelogram Properties- Sides
Opposite sides are parallel
Opposite sides are congruent

7. Parallelogram Properties- Angles
Opposite angles are congruent
Consecutive angles are supplementary m m

8. Parallelogram Properties- Diagonals
Diagonals of a parallelogram meet at the midpoints.
Divide the parallelogram into two congruent triangles

9. Parallelogram- Area
A = bh
Area equals the base times the height.

10. Theorems
A quadrilateral is a parallelogram if any ONE of the following is true:
Both pairs of opposite sides are ||
Both pairs of opposite sides are ≈
A pair of opposite sides is both || and ≈
Both pairs of opposite angles are ≈
Diagonals bisect each other

11. Rectangles A rectangle has: two sets of opposite sides parallel, and
four right angles.
It is also a parallelogram, since it has two pairs of parallel sides.

12. Rectangle Properties- Sides
Opposite sides are parallel
Opposite sides are congruent

13. Rectangle Properties- Angles
Four Right Angles
Opposite angles are congruent
Consecutive angles are supplementary m m

14. Rectangle Properties- Diagonals
Diagonals of a rectangle are congruent.
Diagonals bisect each other.

15. Rectangle - Area
A = bh
Area equals the base times the height.

16. Theorems
If a parallelogram is a rectangle, then the diagonals are congruent.
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

17. Rhombus … A rhombus is a parallelogram with four equal sides.
It is not always a rectangle because a rhombus does not have to have 4 right angles.

18. Rhombus Properties- Sides
All four sides are congruent

19. Rhombus Properties- Angles
Same as all other parallelograms:
Opposite angles are congruent
Consecutive angles are supplementary

20. Rhombus Properties- Diagonals
Diagonals of a rhombus are perpendicular.
Each diagonal bisects the opposite angles.

21. Rhombus- Area
A = ½ d1 d2
Area equals ½ times the first diagonal times the second diagonal.

22. Theorems
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

23. Squares … A square has: four right angles four congruent sides
It is also a
rectangle
parallelogram
rhombus

24. Square Properties Opposite sides are || All sides are ≈
Opposite angles are ≈ (90°)
Consecutive angles are supplementary
Diagonals are ≈
Diagonals bisect each other and angles

25. Square - Area
A = s2
Area equals the side times the side.

26. Trapezoids … Trapezoids only have one pair of parallel sides.
A Trapezoid is NOT a parallelogram. `

27. Parts of a Trapezoid The parallel sides are bases.
The nonparallel sides are legs.
Pairs of base angles share the same base.
M and  H are a pair of base angles.
 A and  T are a pair of base angles.

28. Isosceles Trapezoids Legs are ≈ Both pairs of base angles are ≈
Diagonals are ≈

29. Median of a Trapezoid
Median is a segment that joins the midpoints of the legs.
Parallel to the bases
Length is ½ the sum of the bases median=½ (b1 + b2)

30. Trapezoid - Area A = ½ h(b1 + b2)
Area equals ½ the height times the sum of the bases.

31. Quadrilaterals General Quadrilateral Trapezoid 4 sides, 4 angles
Only 1 pair of parallel sides

32. Quadrilaterals General Quadrilateral Parallelogram Trapezoid
4 sides, 4 angles
Parallelogram
Opposite sides are parallel and congruent
Trapezoid
Only 1 pair of parallel sides

33. Quadrilaterals General Quadrilateral Parallelogram Trapezoid Rectangle
4 sides, 4 angles
Parallelogram
Opposite sides are parallel and congruent
Trapezoid
Only 1 pair of parallel sides
Rectangle
A parallelogram with 4 right angles

34. Quadrilaterals General Quadrilateral Parallelogram Trapezoid Rectangle
4 sides, 4 angles
Parallelogram
Opposite sides are parallel and congruent
Trapezoid
Only 1 pair of parallel sides
Rectangle
A parallelogram with 4 right angles
Square
A rectangle with 4 congruent sides

35. Quadrilaterals General Quadrilateral Parallelogram Trapezoid Rectangle
4 sides, 4 angles
Parallelogram
Opposite sides are parallel and congruent
Trapezoid
Only 1 pair of parallel sides
Rectangle
A parallelogram with 4 right angles
Rhombus
A parallelogram with 4 congruent sides
Square
A rectangle with 4 congruent sides

36. Comparison of Quadrilateral Properties
Parallelogram
Rectangle
Square
Rhombus
Isosceles Trapezoid
Opposite sides ≈
# of pairs
Opposite sides ||
Diagonals ≈
Yes /No
Diagonals perpendicular
Diagonals bisect each other
Diagonals bisect opposite angles
All angles 90°

37. Comparison of Quadrilateral Properties
Parallelogram
Rectangle
Square
Rhombus
Isosceles Trapezoid
Opposite sides ≈
2 pairs
1 pair
Opposite sides ||
Diagonals ≈ No
Yes
Diagonals perpendicular
Diagonals bisect each other
Diagonals bisect opposite angles
All angles 90°

38. Venn Diagram of Quadrilaterals
Parallelograms
Trapezoids
Rectangles
Squares
Rhombi