1. 2/9/15 Unit 8 Polygons and Quadrilaterals Special Parallelograms
Rectangles, Rhombi
and
Squares

2. 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.

3. Properties of Rectangles
If a parallelogram is a rectangle, then its diagonals are congruent.
Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles. E D C B A
Converse:
If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle.

4. 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

5. 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

6. Properties of a Rhombus
Theorem:
The diagonals of a rhombus are perpendicular.
Theorem:
Each diagonal of a rhombus bisects a pair of opposite 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.
10. If AB = 10, then AD = _____ and DC = _____.
11. If CE = 5, then DE = _____.
12. m<ABC = _____.
m<ACD = _____.
m<AED = _____.
10 units
10 units
5 units
90°
45°
90°