Understanding Parallelograms | Properties and Types for Math Enthusiasts

Parallelogram

A parallelogram is a quadrilateral (a polygon with four sides) in which opposite sides are parallel and equal in length

A parallelogram is a quadrilateral (a polygon with four sides) in which opposite sides are parallel and equal in length. In other words, a parallelogram is a shape with two pairs of parallel sides. The opposite angles of a parallelogram are congruent (equal) as well.

Properties of a Parallelogram:
1. Opposite sides are parallel: This means that if we extend one side, it will never intersect the other side. If side AB is parallel to side CD, we write it as AB || CD.
2. Opposite sides are equal in length: The length of side AB is equal to the length of side CD, and the length of side BC is equal to the length of side AD.
3. Opposite angles are congruent: Angle A is congruent to angle C, and angle B is congruent to angle D. We write this as ∠A ≅ ∠C and ∠B ≅ ∠D.
4. Consecutive angles are supplementary: The sum of two consecutive angles in a parallelogram is always 180 degrees. This can be written as ∠A + ∠B = 180° and ∠B + ∠C = 180°.

Types of Parallelograms:
1. Rectangle: A parallelogram with all angles equal to 90 degrees.
2. Square: A parallelogram with all sides equal in length and all angles equal to 90 degrees.
3. Rhombus: A parallelogram with all sides equal in length.
4. Trapezoid: A parallelogram with only one pair of opposite sides being parallel.

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