# Polygons

## Theorem 6-3

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

## Theorem 6-4

If a quadrilateral is a parallelogram, its consecutive angles are supplementary.

## Theorem 6-5

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

## Theorem 6-6

If a quadrilateral is a parallelogram, then its diagonal bisects each other.

## Theorem 6-8

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

## Theorem 6-9

If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

## Theorem 6-10

If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

## Theorem 6-11

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

## Theorem 6-12

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

## Trapezoid and Isosceles Trapezoid Example

MN is half of QR and PS.

You multiply by 2 to get rid of the half.

You combine like terms, then divide to get 6 = x.

## Kite Example

Where angle 1 is, is always 90 because the lines intersect each other.

Angle 2 is 38 + 90 + x = 180 because it is a triangle. Angle 2 is 52.

Angle 3 is 38 because it is congruent to the other angle because the sides are congruent.

Angle 4 is 90 + 53 + x = 180 because it is a triangle. Angle 4 is 37.

Angle 5 is 53 because it is congruent to the other angle because the sides are congruent.

## Embedded Video

Rhombus Song Video

## Works Cited

Because the sides of a parallelogram are equal, you equal them to each other.