Properties, Shapes, Diagonals and Area
A parallelogram is quadrilateral comprised of two pairs of parallel lines. There are several rules involving
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The full size interactive parallelogram has additional features such as the lengths of the diagonals.
Angles of A Parallelogram
Opposite Angles are Congruent
Triangles can be used to prove this rule about the opposite angle.
Consecutive angles are supplementary.
What is the measure of angles A, B and C in parallelogram ABCD?
What is the measure of x, y, z in parallelogram below?
In a parallelogram one of the angles measures 25°, what are the measures of the other angles?
one = 25° (this is the opposite angle)
another = 180-25 = 155° (a consecutive angle)
a third = 180-25 = 155°; (a consecutive angle)
Sides of a Parallelogram
The opposite sides of a parallelogram are congruent.
Triangles can be used to prove this rule about the opposite sides.. To explore these rules governing the sides of a parallelogram use Math Warehouse's interactive parallelogram
What is the value of x and y in the parallelogram below?
Since opposite sides are congruent you can set up the following equations:
2x − 10 = x + 80 and solve for x
x =903y − 4 = y + 20 and solve for y
y = 12
Diagonals of a Parallelogram
What is x and Y?
Since the diagonals bisect each other, y = 16 and x = 22
What is x?
x + 40 = 2x + 18
40 = x +18
40 = x + 18
22 = x