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5-1 Properties of Parallelograms

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5-1 Properties of Parallelograms Ch. 5 Test: Fri Dec. 2 Parallelogram A quadrilateral where both pairs of opposite sides are parallel. Remember your properties for ... – PowerPoint PPT presentation

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Title: 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
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