Rhombus

a parallelogram with four congruent sides

Rectangle

a parallelogram with four right angles

Square

a parallelogram with four congruent sides and four right angles (combination of a rhombus and a rectangle)

Rhombus Theorems

(1) a parallelogram is a rhombus if and only if its diagonals are perpendicular (2) A parallelogram is a rhombus is a rhombus if and only if each diagonal bisects a pair of opposite angles

Rectangle Theorems

(1) A parallelogram is a rectangle if and only if its diagonal are congruent

Trapezoid

a quadrilateral with exactly one pair of parallel sides

Trapezoid's bases

the parallel side

Trapezoid's legs

the nonparallel sides

isosceles trapezoid

the legs of the trapezoid are congruent

Isosceles trapezoid Theorems

(1) a trapezoid is isosceles, then each pair of base angles congruent (2) Atrapezoid is isosceles if and only if its diagonals are congruent

Mid segment theorem for Trapezoids

The midsegment og a trapazoid is parallel to each base and its length is one half the sum of the lengths of the bases

Kite

a quadrilateral that has two pairs of consecutive congruent sides

Kite Theorems

(1) a quadrilateral is a kite, then its diagonals are perpendicular (2) If a quadrilatrilateral is a kite, then exactly one pair of opposite angles are congruent