Parallelogram is generally named by the graphic name followed by four vertices. When using letters to represent quadrangles, be sure to indicate vertices clockwise or counterclockwise.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram have the same length, and the diagonals of the parallelogram are equal.
On the contrary, a quadrilateral with only one pair of parallel sides is a trapezoid. The three-dimensional correspondence of a parallelogram is a parallelepiped.
Extended data
decision
1, two groups of parallelograms with opposite sides are parallelograms (definition judgment method);
2. A group of quadrilaterals with parallel and equal opposite sides are parallelograms;
3. Two groups of quadrangles with equal opposite sides are parallelograms;
4. Two groups of quadrangles with equal diagonal angles are parallelograms (judging that two groups of opposite sides are parallel);
5. The quadrilateral whose diagonals bisect each other is a parallelogram.
Supplement: Condition 3 holds only if it is a planar quadrilateral. If it is not a plane quadrilateral, even two sets of quadrilaterals with equal opposite sides are not parallelograms.
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