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Polygons

Parallelogram Properties

A parallelogram is a quadrilateral that has two pairs of parallel sides.

There are several rules involving the angles, the sides or the diagonals of a parallelogram.

Angles of a parallelogram
• Opposite angles of a parallelogram are congruent.
• Consecutive angles of a parallelogram are suppementary.

Sides of a parallelogram

• The opposite sides of a parallelogram are congruent.

Diagonals of a parallelogram

• The diagonals of a parallelogram bisect each other.

 Find x and y

Consecutive angles are supplentary:
(6x+10)+(2x+10)=180
8x+20=180
8x=160
x=20º

Opposite angles are congruent:
2(20)+10=y
y=50º

 Find the perimeter P

Opposite sides are congruent:
20=x+3
x=17

P=20+2(17)+17+3+2(17)=108 units.