1. 2.19 Classifying Parallelograms
Bell Ringer
1. WXYZ is a parallelogram. Name an angle congruent to ∠XYZ.                  
∠WZY
∠XWY
∠XWZ
∠ZWY
2. ABCD is a parallelogram. If m∠CDA = 56, then m∠ABC =   .                 66
134
124 56
2.19 Classifying Parallelograms

2. 2.19 Classifying Parallelograms
Rectangles
Definition:
A rectangle is a with four right angles.
A rectangle is a special type of
Thus a rectangle has all the properties of a .
Opp. sides are
Opp. sides are congruent.
Opp. angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.
2.19 Classifying Parallelograms

3. Properties of Rectangles
Theorem:
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.
2.19 Classifying Parallelograms

4. 2.19 Classifying Parallelograms
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
2.19 Classifying Parallelograms

5. 2.19 Classifying Parallelograms
Rhombus
Definition:
A rhombus is a parallelogram with four congruent sides. ≡ ≡
Since a rhombus is a parallelogram the following are true:
Opp. sides are parallel.
Opp. sides are congruent.
Opp. angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other
2.19 Classifying Parallelograms

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.
2.19 Classifying Parallelograms

7. 2.19 Classifying Parallelograms
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
2.19 Classifying Parallelograms

8. 2.19 Classifying Parallelograms
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.
Opp. sides are parallel.
4 right angles.
4 congruent sides.
Consecutive angles are supplementary.
Diagonals are congruent.
Diagonals bisect each other.
Diagonals are perpendicular.
Each diagonal bisects a pair of opp. angles.
2.19 Classifying Parallelograms

9. 2.19 Classifying Parallelograms
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°
2.19 Classifying Parallelograms

10. 2.19 Classifying Parallelograms
Summary
Write at least 3 sentences
No Homework
2.19 Classifying Parallelograms

11. 2.19 Classifying Parallelograms
QUADRILATERAL FAMILY TREE
QUADRILATERALS
KITE
TRAPEZOID
PARALLELOGRAMS
ISOSCELES TRAPEZOID
RECTANGLE
RHOMBUS
SQUARE
2.19 Classifying Parallelograms