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Name _______________________________________ Date __________________ Class __________________ Section 6.3 Conditions for Parallelograms You can show that a quadrilateral is a parallelogram by using any of the conditions listed below. Conditions for Parallelograms • Both pairs of opposite sides are parallel (definition). • One pair of opposite sides is parallel and congruent. • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • The diagonals bisect each other. • One angle is supplementary to both its consecutive angles. Determine whether each quadrilateral must be a parallelogram. State the reason if it is. Class Example 1: Class Example 2 Determine whether each quadrilateral must be a parallelogram. Justify your answer. 3. 4. ________________________________________ ________________________________________ ________________________________________ ________________________________________ 6. 5. ________________________________________ ________________________________________ ________________________________________ ________________________________________ 7. 8. ________________________________________ ________________________________________ ________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date __________________ Class __________________ Determine whether the figure is a parallelogram for the given values of the variables. Explain your answers. 9. x 9 and y 11 10. a 4.3 and b 13 Show that the quadrilateral with the given vertices is a parallelogram by using the given definition or theorem. 11. J(2, 2), K(3, 3), L(1, 5), M(2, 0) Both pairs of opposite sides are parallel. 12. N(5, 1), P(2, 7), Q(6, 9), R(9, 3) Both pairs of opposite sides are congruent. Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry