properties of parallelograms
Properties of Parallelograms:
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Properties of Parallelograms:
1. Opposite sides are parallel: In a parallelogram, the opposite sides are always parallel. This means that if you extend the sides of a parallelogram, they will never intersect.
2. Opposite sides are congruent: In a parallelogram, the opposite sides are equal in length. Therefore, if you measure the lengths of the opposite sides of a parallelogram, you will find that they are equal.
3. Opposite angles are congruent: In a parallelogram, the opposite angles are equal in measure. This means that if you measure the angles formed by the intersection of the sides in a parallelogram, you will find that they are equal.
4. Consecutive angles are supplementary: In a parallelogram, the consecutive angles (angles formed by two adjacent sides) are supplementary, meaning that their sum is 180 degrees. Therefore, if you measure the consecutive angles in a parallelogram, their sum will always be 180 degrees.
5. Diagonals bisect each other: The diagonals of a parallelogram intersect at their midpoints. This means that each diagonal divides the parallelogram into two congruent triangles. Additionally, the diagonals of a parallelogram are equal in length.
6. Opposite sides are both congruent and parallel: This is a unique property of parallelograms. Not only are the opposite sides parallel and congruent, but they are also congruent to each other. This property distinguishes parallelograms from other quadrilaterals.
7. The sum of all internal angles is 360 degrees: The sum of all the angles inside a parallelogram is always 360 degrees. This property holds true for any quadrilateral, including parallelograms.
These properties are useful in solving various problems involving parallelograms, such as finding missing side lengths or angles, determining congruence, or proving specific geometric relationships.
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