Parallelograms

What is a Parallelogram?

*quadrilateral *2 pairs of parallel sides adjacent sides equal 180
*opposite sides are equal in length * 360 inteorer angles
*diaganals intersect at a 90 angle *AlAs *AEAs *CIAs


Area of a Parallelogram

*Area=base(height) *twice the area of a triangle
*the area is the inside of the parallelogram
*area is equal to the magnitue of the (vector cross product)


Perimeter of Parallelograms

*Height+Height+Length+Length=perimeter

Types of Parallelograms

*Rhomboid-opposite sides are parallel, adjacent sides are unequal, no right angles
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*Rectangle-4 right angles, opposite sides are parallel, and opposite sides are equal
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*Rhombus- sides are equal in length are parallel
external image rhombus.svg.png

*Square-4 right angles, opposite sides are equal and are parallel

external image 536px-SQUARE_SHAPE.svg.png

Diagonals of Parallelograms

*p=√a squared+b squared-2ab(cosA)
*q=√ a squared+b squared-2ab(cosB)
*simplified- p squared+q squared=2(a squared+b squared)
*met in the center of the parallelogram


History of Parallelograms

*Robert Owen created the first parallelogram in 1820
*Diagonals were founded by Casey in 1888. *later on Beyer simplified it in 1987


Parallelogram Law

*ABC be a parallelogram with side lengths U,V and who's diagonals have lengths d1, and d2
*2u squared+2v squared=d1 squared+d2 squared