Parallelograms are geometric figures with congruent and parallel opposite sides, equal opposite angles, and supplementary adjacent angles. They feature diagonals that bisect each other, creating congruent triangles. Special types include rhombuses, rectangles, and squares, each with unique properties. Understanding these shapes is crucial for spatial reasoning and problem-solving in geometry.
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Parallelograms have four sides with two pairs of opposite sides that are equal and parallel to each other
Notation for parallelograms
Parallelograms are denoted by four letters, indicating parallel and equal sides
Angle relationships in parallelograms
Opposite angles are congruent and consecutive angles are supplementary in parallelograms
When one angle is a right angle, all angles in a parallelogram must be right angles, making it a rectangle
The diagonals of a parallelogram bisect each other and intersect at a point equidistant from the vertices
Each diagonal divides the parallelogram into two congruent triangles
The properties of diagonals are frequently used in geometric proofs and problem-solving
The area of a parallelogram is calculated by multiplying the base by the height
The formula for calculating the area of parallelograms is essential in various applications in geometry and related fields
The base and height of a parallelogram are always at right angles to each other
A parallelogram with all sides equal in length and diagonals that bisect each other at right angles
A parallelogram with all interior angles being right angles and congruent diagonals
A parallelogram that is both a rhombus and a rectangle, with all sides equal in length and all angles right angles
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Parallelogram opposite sides
Opposite sides are congruent and parallel.
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Parallelogram opposite angles
Opposite angles are equal (∠A = ∠C, ∠B = ∠D).
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Parallelogram adjacent angles
Adjacent angles are supplementary (∠A + ∠B = 180°, ∠C + ∠D = 180°).
