Parallelograms — A Complete Guide for Grade 8
Big Idea: A parallelogram is a quadrilateral (4-sided polygon) in which both pairs of opposite sides are parallel. This single condition leads to a rich set of properties involving sides, angles, and diagonals.
📐 Formal Definition
A quadrilateral $ABCD$ is a parallelogram if and only if:
$AB \parallel CD$ and $BC \parallel AD$
We write: $ABCD$ is a parallelogram, or $\square ABCD$.
✅ Key Properties
- Opposite sides are equal: $AB = CD$ and $BC = AD$
- Opposite angles are equal: $\angle A = \angle C$ and $\angle B = \angle D$
- Consecutive angles are supplementary: $\angle A + \angle B = 180°$
- Diagonals bisect each other: If diagonals $AC$ and $BD$ meet at $O$, then $AO = OC$ and $BO = OD$
- Each diagonal divides the parallelogram into two congruent triangles.