Parallelogram
A parallelogram is a quadrilateral (a four-sided polygon) with opposite sides that are parallel
A parallelogram is a quadrilateral (a four-sided polygon) with opposite sides that are parallel. This means that the opposite sides of the parallelogram do not intersect and are of equal length. In addition, the opposite angles of a parallelogram are equal.
Key properties of a parallelogram include:
1. Opposite sides are parallel: This means that if you extend the adjacent sides of a parallelogram, they will never intersect.
2. Opposite sides are equal: The lengths of the opposite sides of a parallelogram are equal. This symmetry distinguishes parallelograms from other quadrilaterals.
3. Opposite angles are equal: The measure of the opposite angles of a parallelogram are equal. This means that if you label the angles of a parallelogram as A, B, C, and D, then angle A is equal to angle C, and angle B is equal to angle D.
4. Consecutive angles are supplementary: The consecutive (adjacent) angles of a parallelogram add up to 180 degrees. For example, if angle A measures 60 degrees, then angle B would measure 120 degrees.
5. Diagonals bisect each other: The diagonals of a parallelogram are the line segments that connect opposite corners of the parallelogram. These diagonals bisect each other, meaning that they intersect at their midpoints, dividing each diagonal in half.
6. Opposite sides and angles can be used to determine congruence: If all pairs of opposite sides and angles in two parallelograms are congruent (equal), then the two parallelograms are congruent.
Some special types of parallelograms include:
1. Rectangle: A parallelogram in which all angles are right angles (90 degrees). Opposite sides of a rectangle are equal in length.
2. Rhombus: A parallelogram in which all sides are equal in length. Opposite angles of a rhombus are equal.
3. Square: A parallelogram in which all sides are equal in length and all angles are right angles. A square is both a rectangle and a rhombus.
You can calculate the area of a parallelogram by multiplying the base (length of one side) by the height (perpendicular distance between the base and its opposite side).
The perimeter of a parallelogram is the sum of all four sides. To find the perimeter, you can add the lengths of all four sides together.
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