6-2 Properties of Parallelograms

Area

Area of Parallelogram A = base x height

height

base

Proof1.

2.

3.

4.

5.

6.

7.

8.

CB

A D

Given: ABCD is a parallelogramProve: AB DC BC DA <A <C

Proof1.

2.

3.

4.

5.

6.

7.

E

CB

A D

Given: ABCD is a parallelogramProve: EA EC EB ED

TheoremsOpposite sides of a parallelogram are congruent.

Opposite angles of a parallelogram are congruent.

Consecutive angles of a parallelogram are supplementary.

Diagonals of a parallelogram bisect each other.

TheoremsIf three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

AD BE CF and AB BC then DE EF

D

E

FC

B

A

Examples1) Find area of the

parallelogram2) Find area of a parallelogram

with vertices (-5,-3), (-2,3), (2,3) & (-1,-3).

15

12

10

A

D

B

C

Examples3) If AB=3x + 11, BC = 2x

+ 19 and CD = 7x – 17,

find x.

4) If m<BAD = y and

m<ADC = 4y – 70, find y.

5) If m<ABC=2x + 100 and

m<ADC=6x + 84, find

m<BCD.

P

A

D

B

C

Examples

6) If m<BCD=80 and

m<CAD=34, find

m<ACD.

7) If AP=3x, BP=y, CP=6x

- 42, and DP=27 - 2y,

find x &y.

P

A

D

B

C

Examples8) Find EH.

2.52

2

2

H

P

O

E

J

L

K

M

Example: Honors Geometry

Statements Reasons1.2.3.4.5.6.

Given: ABCD is parallelogram BE DF

Prove: AF CE

E

F

A

B C

D