
Properties of a Parallelogram:
1. In a parallelogram any two opposite sides are equal. THEOREMS: 1. A quadrilateral is a parallelogram, then its opposite sides are congruent; If ABCD is a parallelogram, then AB @ CD and BC @ AD 2. A quadrilateral is a parallelogram, then its opposite angles are congruent; If ABCD is a parallelogram, then ÐA @ ÐC and ÐB @ ÐD. 3. A quadrilateral is a parallelogram, then its consecutive angles are supplementary; Ðx + Ðy = 180^{0} 4. A quadrilateral is a parallelogram, then its diagonals bisect each other. 5. One pair of opposite sides are equal and parallel; Special types of parallelograms: rhombus, rectangle, square A quadrilateral is a rhombus if and only if it has four congruent sides. A quadrilateral is a rectangle if and only if it has four right angles. A quadrilateral is a square if and only if it is a rhombus and rectangle. A parallelogram is a rhombus, if and only if its diagonals are perpendicular. A parallelogram is a rhombus, if and only if each diagonal bisects a pair of opposite angles. A parallelogram is a rectangle, if and only if its diagonals are congruent.
Example: Directions: Draw a parallelogram and answer the following questions. 1) Parallelogram of lengths 5, 12, 5, x+4 cm. Find the value of x. 2) Parallelogram of angles 60^{0}, 120^{0},60^{0}, 2x^{0}. Find the value of x. 3) Parallelogram with supplementary angles of 2x^{0}, 4x^{0}. Find the value of x. 