Opposite angles of a parallelogram are equal, a fundamental characteristic that distinguishes this quadrilateral from many others. In any parallelogram, the two angles that do not share a side are congruent, meaning they have identical measures. This equality arises from the definition of a parallelogram as a quadrilateral with both pairs of opposite sides parallel, and it underlies many geometric arguments and practical applications.
What Is a Parallelogram?
A parallelogram is a four‑sided polygon (quadrilateral) in which each pair of opposite sides is parallel. The parallel condition can be written as AB ∥ CD and BC ∥ AD for vertices labeled in order. This simple definition leads to a cascade of properties, including the equality of opposite angles, the bisecting diagonals, and the supplementary relationship between consecutive angles.
Short version: it depends. Long version — keep reading.
Key Properties of a Parallelogram
- Opposite sides are equal in length.
- Opposite angles are congruent.
- Consecutive angles are supplementary (their sum is 180°).
- Diagonals bisect each other, meaning each diagonal cuts the other into two equal segments.
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