Classifying Quadrilaterals - ISEE Lower Level: Quantitative Reasoning

A quadrilateral with both pairs of opposite sides parallel. This property ensures opposite sides never intersect and form the basis for parallelogram classification.

A quadrilateral with exactly $1$ pair of parallel sides. This definition distinguishes trapezoids from parallelograms by limiting parallel sides to one pair, as per common ISEE usage.

A trapezoid with congruent non-parallel sides (legs). Equal legs provide symmetry, leading to congruent base angles and diagonals in this trapezoid subtype.

A quadrilateral with $2$ distinct pairs of adjacent congruent sides. Adjacent equal sides create two pairs meeting at vertices, defining the kite's distinctive shape.

A quadrilateral with $4$ right angles. Four right angles ensure all corners are $90^\circ$, classifying it as a rectangle regardless of side lengths.

A quadrilateral with all $4$ sides congruent. All sides equal in length defines the rhombus, with properties like perpendicular diagonals following from this.

A quadrilateral with $4$ congruent sides and $4$ right angles. Combining equal sides and right angles integrates properties of both rhombus and rectangle into a square.

Opposite sides are parallel and congruent. In parallelograms, opposite sides maintain parallelism and equality due to the parallel property.

Opposite angles are congruent. The parallel sides in a parallelogram force opposite angles to be equal by corresponding angles theorem.

A polygon with exactly $4$ sides. This is the standard geometric definition that specifies the number of sides for classification as a quadrilateral.

The diagonals bisect each other. Diagonals in a parallelogram intersect at their midpoints due to the symmetry of parallel sides.

They are congruent and bisect each other. Rectangles inherit bisecting from parallelograms, with right angles ensuring diagonal equality by Pythagoras.

They are perpendicular and bisect each other. Equal sides in a rhombus cause diagonals to be perpendicular and halve each other at the intersection.

They are congruent, perpendicular, and bisect each other. Squares combine rectangle's equal diagonals with rhombus's perpendicularity and bisecting properties.

They are perpendicular, and one diagonal bisects the other. In a kite, the unequal pairs of sides result in perpendicular diagonals where one is the axis of symmetry bisecting the other.

Each pair of base angles is congruent. Symmetry from equal legs in an isosceles trapezoid makes angles adjacent to each base equal.

The diagonals are congruent. Equal non-parallel sides in an isosceles trapezoid lead to congruent diagonals by symmetry.

Parallelogram. Two pairs of parallel opposite sides uniquely identify a quadrilateral as a parallelogram.

Rectangle. Four right angles define a rectangle, and unequal sides distinguish it from a square.

Rhombus. All equal sides define a rhombus, and non-right angles distinguish it from a square.

Square. Equal sides and right angles together necessitate a square as the only matching quadrilateral.

Trapezoid. Exactly one pair of parallel sides classifies it as a trapezoid, excluding parallelograms.

Kite. Two pairs of adjacent equal sides uniquely identify a kite, distinguishing from other quadrilaterals.