5.J.1 — Classify quadrilaterals by properties.
Step 01 of 04
A quadrilateral is any 4-sided polygon. Different special types add specific properties.
| Parallelogram | →both pairs of opposite sides parallel |
| Rectangle | →parallelogram with 4 right angles |
| Rhombus | →parallelogram with 4 equal sides |
| Square | →rectangle AND rhombus |
| Trapezoid | →EXACTLY one pair of parallel sides |
| Kite | →2 pairs of consecutive equal sides |
Step 02 of 04
Properties chain.
| Square has | →4 equal sides + 4 right angles + parallelogram properties |
| Rectangle has | →4 right angles + parallelogram properties |
| Rhombus has | →4 equal sides + parallelogram properties |
| Parallelogram has | →opposite sides parallel + opposite sides equal + opposite angles equal |
Step 03 of 04
Each special type INHERITS the properties of its parent. Every square IS a rectangle (because a square has 4 right angles + opposite sides parallel).
Step 04 of 04
Common misconception. A rectangle is NOT a square (in general — only squares are squares). But every square IS a rectangle.
Key insight
Quadrilateral classification is a hierarchy: square ⊂ rectangle, rhombus ⊂ parallelogram. Each special type adds properties to its parent's. Read carefully: "rectangle" doesn't mean "square," but a square IS a rectangle.