Classifying Quadrilaterals – Flow Chart Reference

Classify a quadrilateral as a trapezoid, kite, parallelogram, rhombus, rectangle, or square using coordinate-geometry tests.

Apply the slope formula to determine whether pairs of sides are parallel or perpendicular.

Apply the distance formula to determine whether sides or diagonals are congruent.

Follow a decision-tree structure to narrow a shape's classification step by step from a general quadrilateral to a specific type.

Use the shorter chart (page 2) for a unit limited to parallelograms, rhombi, rectangles and squares; use the fuller chart (page 3) once trapezoids and kites are also in scope.

Keep the printed slope and distance formula box visible as a quick reference while students work through either chart.

Coordinate-geometry classification — students trace a decision tree from "how many pairs of opposite sides are parallel?" to a final quadrilateral type.

Slope formula application — students test whether sides are parallel (equal slopes) or perpendicular at each relevant branch point.

Distance formula application — students test whether sides or diagonals are congruent by comparing computed lengths.

Property-based justification — students name a shape from its defining property, such as "all 4 sides are congruent" for a rhombus, rather than by appearance alone.