Geometry Postulates and Theorems
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Parallelogram Rectangle
If both pairs of opposite sides of a quadrilateral are congruent,
then the quadrilateral is a perallelogram.
The diagonals of a rectangle are congruent
.If both pairs of opposite angles of a quadrilateral are congruent,
then the quadrilateral is a parallelogram
If the diagonals of a parallelogram are congruent,
then the parallelogram is a rectangle.
If one pair of opposite sides of a quadrilateral is both parallel and congruent,
then the quadrilateral is a parallelogram.
If one angle of a parallelogram are is a right angle,
then the parallelogram is a rectangle.
If the diagonals of a quadrialateral bisect each other,
then the quadrilateral is a parallelogram.
The area of a rectangle is the product of the base and the height. (A = bh)
The area of a parallelogram is the product of the base and the height.(A = bh)  
The opposite sides of a parallelogram are congruent.
The opposite angles of a parallelogram are congruent.
The diagonals of a parallelogram bisect each other.
Trapezoid Rhombus and Square
The area of a trapezoid is the product of the height and themean of the bases. A
(A = 1/2 (b1 + b2)h)
The diagonals of a rhombus are perpendicular.
The base angles of an isosceles trapezoid are congruent. If the diagonals of a parallelogram are perpendicular,
then the parallelogram is a rhombus.
If the base angles are congruent, then the trapezoid is isosceles. If two consecutive sides of a parallelogram are congruent
then the parallelogram is a rhombus.
Kite The area of a square is the square of the length of one side. (A = s2)
Exactly one diagonal of a kite is a line of symmetry for the kite and the perpendicular bisector of the other diagonal.