Geometry Postulates and Theorems textbook tutorials - definitions - constructions - postulates and theorems - internet activities and resources mathematical logic symmetry and similarity points, lines and planes parallel lines triangles quadrilaterals polygons circles 3-Dimensional Geometry 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.