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.

Point out the "skip to here" shortcut so students who can already justify a shape's defining property algebraically don't have to work through every branch.

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

Have students fill in the name and hour fields in the header, since each chart is formatted as an individual student page rather than a shared class handout.

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.