5-1 Properties of Parallelograms

1
5-1 Properties of Parallelograms

• Ch. 5 Test Fri Dec. 2

2
Parallelogram

• A quadrilateral where both pairs of opposite
  sides are parallel.

3
Remember your properties for parallel lines
x
z
y

• x and y are SSI angles
• Therefore, x and y are supplements
• x y 180
• x and z are also SSI therefore also supplements
• x z 180
• So, y z
• Supps of the same angle are congruent.

4
Theorem
x
y

• Opposite angles of a parallelogram are congruent.
  (x and Y are opposite angles)
• Opposite sides of a parallelogram are congruent.
• Diagonals of a parallelogram bisect each other.

5
Example

• Given BC 8, AB 15, EC 8, DB 18.
• Find AD
• DC
• AE
• AC
• BE
• DE

8
A
15
B
15
8
E
8
8
16
18
9
C
D
9
6
Example

• Given Angle ADC 82, Angle EDC 26
• Find angles
• ADE
• ABC
• EBC
• BCD
• BEC

A
B
56
82
82
56
9
E
56
56
8
8
56
98
82
98
26
56
C
D
7
TOOon whiteboards

• If ABCD is a parallelogram, what is the length of
  segment BD?
• A) 10
• B) 11
• C) 12
• D) 5

8
TOOon WBs

• Solve for x, y and z

12
130
10
x
y
z
9
Homework

• Pg. 169-170 1-12, 16 (4 steps), 19-23
• Flashcards
• Definition of Parallelogram
• 3 Theorems