1. Special Quadrilaterals

2. Special Quadrilaterals (four sides)
A parallelogram has two pairs of opposite sides parallel.
A rectangle has two pairs of opposite sides parallel and four right angles.
A square has two pairs of opposite sides parallel, four right angles, and four equal sides.
A rhombus has two pairs of opposite sides parallel and four equal sides.
A trapezoid has one pair of parallel sides.

3. Venn Diagram: Quadrilaterals
Parallelograms in White Circle
Rectangles
Squares
Trapezoids
Rhombuses

4. Rectangles Definition:
A rectangle is a parallelogram with four right angles.
A rectangle is a special type of parallelogram.
Thus a rectangle has all the properties of a parallelogram.
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.

5. Examples If AE = 3x +2 and BE = 29, find the value of x.
If AC = 21, then BE = _______.
If m<1 = 4x and m<4 = 2x, find the value of x.
If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6.
x = 9 units
10.5 units
x = 18 units 6 5 4 3 2 1 E D C B A
m<1=50,
m<3=40,
m<4=80,
m<5=100,
m<6=40

6. Rhombus ≡ ≡ Definition:
A rhombus is a parallelogram with four congruent sides. ≡ ≡
Since a rhombus is a parallelogram the following are true:
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other
Diagonals bisect the angles.

7. Rhombus Examples Given: ABCD is a rhombus. Complete the following.
If AB = 9, then AD = ______.
If m<1 = 65, the m<2 = _____.
m<3 = ______.
If m<ADC = 80, the m<DAB = ______.
If m<1 = 3x -7 and m<2 = 2x +3, then x = _____.
9 units
65°
90°
100° 10

8. Square
Definition:
A square is a parallelogram with four congruent angles and four congruent sides.
Since every square is a parallelogram as well as a rhombus and rectangle, it has all the properties of these quadrilaterals.
Opposite sides are parallel.
Four right angles.
Four congruent sides.
Consecutive angles are supplementary.
Diagonals are congruent.
Diagonals bisect each other.
Diagonals are perpendicular.
Each diagonal bisects a pair of opposite angles.

9. Squares Examples Given: ABCD is a square. Complete the following.
If AB = 10, then AD = _______ and DC = _______.
If CE = 5, then DE = _____.
m<ABC = _____.
m<ACD = _____.
m<AED = _____.
10 units
10 units
5 units
90°
45°
90°