What is Parallelogram? — Mathematics

Definition 52.7 Primary & Middle School Mathematics · Chapter 52 — Central Symmetry and Parallelograms

A parallelogram is a quadrilateral whose diagonals cross at their common midpoint. That crossing point is then a center of symmetry of the figure: each vertex is the half-turn image of the opposite vertex.

A parallelogram and its center O: the diagonals (red) cut each other at their midpoints, opposite sides are parallel and equal (tick marks). — A parallelogram and its center $O$ : the diagonals (red) cut each other at their midpoints, opposite sides are parallel and equal (tick marks).

Examples

Example 52.10

$ABCD$ has $(AB) \parallel (CD)$ and $AB = CD = 5$ cm. Criterion 3 applies: $ABCD$ is a parallelogram — so without any further measuring we also know $AD = BC$ , $(AD) \parallel (BC)$ , and that its diagonals cut each other in their middle.

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Examples

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