Quadrilateral Properties,Definitions, & Proofs

quadrilateral definition

4 sides

square definition

all sides and angles are congruent

rhombus definition

all sides are congruent

trapezoid definition

one set of parallel sides

parallelogram definition

two sets of parallel sides

rectangle definition

all angles are equal

isosceles trapezoid definition

one set of parallel sides and one set of congruent sides

trapezoid properties

1. one set of parallel sides

2. 2 sets of same side interior angles (supplementary)

isosceles trapezoid properties

1. diagonals are congruent

2. base angles are congruent

parallelogram properties

1. two sets of opposite congruent sides

2. two sets of opposite congruent angles

3. diagonals bisect each other

rectangle properties

1. is a parallelogram (collective def and properties)

2. diagonals are congruent

rhombus properties

1. is a parallelogram (collective def and properties)

2. diagonals are perpendicular

square properties

1. equiangular

2. congruent sides

3. congruent diagonals

proof of trapezoid

4 slope formulas (2 parallel and 2 not parallel sets of sides)

proof of isosceles trapezoid

4 slope formulas and 2 distance formulas (to prove congruent diagonals)

proof of parallelogram

6 distance formulas (prove two sets of congruent sides, not congruent diagonals)

proof of rectangle

6 distance formulas (prove two sets of congruent sides, AND congruent diagonals)

proof of rhombus

6 distance formulas (prove four congruent sides, not congruent diagonals)

proof of square

6 distance formulas (prove four congruent sides, AND congruent diagonals)