Quadrilateral Theorems

Home , Parallelogram, Quadrilateral, Rectangle, Rhombus, Trapezoid

 If a quadrilateral is a TRAPEZOID then, 1. at least one pair of opposite sides are parallel(bases)

 If a quadrilateral is an ISOSCELES TRAPEZOID then, 1. At least one pair of opposite sides are parallel (bases) 2. the non-parallel sides are congruent 3. both pairs of base angles are congruent 4. diagonals are congruent

 If a quadrilateral is a PARALLELOGRAM then, 1. opposite sides are congruent 2. opposite sides are parallel 3. opposite angles are congruent 4. consecutive angles are supplementary 5. the diagonals bisect each other

 If a quadrilateral is a RECTANGLE then, 1. All properties of Parallelogram PLUS 2. All the angles are right angles 3. The diagonals are congruent

 If a quadrilateral is a RHOMBUS then, 1. All properties of Parallelogram PLUS 2. the diagonals bisect the vertices 3. the diagonals are perpendicular to each other 4. all four sides are congruent

 If a quadrilateral is a SQUARE then, 1. All properties of Parallelogram PLUS 2. All properties of Rhombus PLUS 3. All properties of Rectangle Proving a Trapezoid:  If a QUADRILATERAL has at least one pair of parallel sides, then it is a trapezoid.

Proving an Isosceles Trapezoid: 1st prove it’s a TRAPEZOID  If a TRAPEZOID has ____(insert choice from below) ______then it is an isosceles trapezoid. 1. congruent non-parallel sides 2. congruent diagonals 3. congruent base angles

Proving a Parallelogram:  If a quadrilateral has ____(insert choice from below) ______then it is a parallelogram. 1. both pairs of opposite sides parallel 2. both pairs of opposite sides ≅ 3. one pair of opposite sides that are parallel and congruent 4. both pairs of opposite angles ≅ 5. diagonals that bisect each other

Proving a Rectangle:  If a quadrilateral is equiangular, then it is a rectangle 1st prove it’s a parallelogram  If a PARALLELOGRAM has ____(insert choice from below) ______then it is a rectangle. 1. one right angle 2. congruent diagonals

Proving a Rhombus:  If a quadrilateral is equilateral, then it is a rhombus 1st prove it’s a parallelogram  If a PARALLELOGRAM has ____(insert choice from below) ______then it is a rhombus. 1. two consecutive sides that are congruent 2. diagonals that are perpendicular to each other

Proving a Square:  If a RECTANGLE has two consecutive sides that are congruent, then it is a Square  If a RHOMBUS has one right angle, then it is a square.