Quadrilaterals — A Complete Guide for Grade 8
Definition: A quadrilateral is a closed polygon with exactly four sides, four vertices, and four angles. The word comes from Latin: quadri (four) + latus (side).
🔑 Fundamental Property
The angle sum property of any quadrilateral states:
$$ \angle A + \angle B + \angle C + \angle D = 360° $$
This can be proven by drawing a diagonal, which divides the quadrilateral into two triangles. Since each triangle has an angle sum of $180°$:
$180° + 180° = 360°$
📐 Key Terminology
- Sides: The four line segments forming the boundary
- Vertices: The four corner points (A, B, C, D)
- Diagonals: Line segments connecting non-adjacent vertices (AC and BD)
- Adjacent sides: Sides sharing a common vertex
- Opposite sides: Sides that do not share a vertex