Properties of Quadrilaterals

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High School Math based on the topics required for the Regents Exam conducted by NYSED.

Properties and Parts of Trapezoids :
Trapezoids are one of the most common quadrilaterals. A trapezoid has one pair of parallel sides. A more specific type of trapezoid is called an isosceles trapezoid. In addition to one pair of parallel sides, isosceles trapezoid properties include congruent legs, base angles and diagonals. The differences between trapezoids, parallelograms, and kites. Parallelogram Properties :
Properties of parallelograms often show up in geometric proofs and problems. Parallelogram properties apply to rectangles, rhombi and squares. In a parallelogram, opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary and diagonals bisect each other. Other important polygon properties to know are trapezoid properties, and kite properties. Rectangle and Square Properties :
Squares and rectangles are special types of parallelograms with special properties. A square is a type of equiangular parallelogram and square properties include congruent diagonals and diagonals that bisect each other. A rectangle is a type of regular quadrilateral. Rectangle properties include (1) diagonals that are congruent, (2) perpendicular diagonals that bisect each other and (3) diagonals that bisect each of the angles. Properties that differentiate a rectangle from a parallelogram. Two example problems to demonstrate how to solve for interior angles Rhombus Properties :
Properties of rhombi often show up in geometric proofs and many other types of problems. All parallelogram properties apply to rhombus properties since a rhombus is a type of parallelogram. In a rhombus, there are (1) two pairs of parallel sides, (2) four sides that are all congruent to each other, (3) diagonals that bisect the angles, and (4) diagonals that are perpendicular bisectors of each other.