1. Properties of Quadrilaterals
Any four sided polygon is a quadrilateral.
We’ll study special quadrilaterals in this section:
Trapezoid (U.S) or Trapezium (U.K)
Parallelogram
Rhombus
Rectangle
Square
Kite

2. A KITE 2 pair of consecutive congruent sides
Opposite sides are NOT congruent
Diagonals are perpendicular
Notice only ONE diagonal
is bisected

3. Properties of a trapezoid
A trapezoid has one and only one pair of parallel sides.

4. Properties of parallelograms
Opposite sides of a parallelogram are parallel
Opposite sides are congruent
Opposite angles of a parallelograms are congruent.
Diagonals of a parallelogram bisect each other
Consecutive angles of a parallelogram are supplementary
supplementary

5. Properties of a Rhombus (Rhombi)
A rhombus is a parallelogram (this means it has ALL of the characteristics of a parallelogram)
In addition:
A rhombus has four congruent sides
The diagonals of a rhombus are perpendicular
The diagonals bisect
opposite angles

6. Properties of Rectangles
A rectangle is a parallelogram (this means it has ALL the characteristics of a parallelogram)
IN ADDITION:
Four right angles
The diagonals of a rectangle are congruent and they bisect each other

7. Properties of Squares
A square is a parallelogram, a rectangle, and a rhombus (It has ALL those characteristics!!!)
Has four congruent sides
Has four right angles
The diagonals of a square:
bisect each other
are congruent
are perpendicular.
Bisect opposite angles

8. Practice Problems. Study Carefully and then take your test.
Is this statement true or false. Explain your answer.
All rhombuses are squares
A rhombus has four congruent sides, but some may or may not have right angles. The statement is false.

9. Is this statement true or false. Explain your answer.
Some trapezoids are squares
A square has two sets of parallel sides, but a trapezoid has only one set of parallel sides. The statement is false.

10. Is this statement true or false. Explain your answer.
Some parallelograms are squares.
A square has all the properties of a parallelogram, so some parallelograms do have equal sides and right angles; however, some do not. The statement is true.

11. Is this statement true or false. Explain your answer
All squares are rectangles
A square has four right angles. A rectangle also has four right angles. So a square is a rectangle. The statement is true.

12. Is this statement true or false. Explain your answer
All rectangles are squares
A square has four right angles and four (2 pairs of) congruent sides. A rectangle has four right angles and 2 (a pair of) congruent sides. The statement is false.

13. Is this statement true or false. Explain your answer
Some rectangles are squares.
If the rectangle has four congruent sides, then it is a square. The statement is true.

14. Classwork Answer these questions. Give your reasons.
(1.) A quadrilateral with four right angles and four congruent sides is called…………………….
(2.) A quadrilateral with two four right angles and two congruent sides is called………………………..
(3.) A quadrilateral with exactly one pair of parallel sides is called………………..
(4.) Name any three quadrilaterals with exactly two pairs of parallel sides
(5.) True or False: All quadrilaterals are parallelograms.
(6.) True or False: Every parallelogram is a rectangle.