6.3 Conditions for Parallelograms

Conditions for Parallelograms The figure is a parallelogram if… Both pairs of opposite sides are congruent Both pairs of opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other One pair of opposite sides are both parallel and congruent

Examples 1) Show that JKLM is a parallelogram for a = 3 and b = 9.

Examples: 2) Show that PQRS is a parallelogram for x = 10 and y = 6.5.

Example 3) Show that PQRS is a parallelogram for a = 2.4 and b = 9.

Example 4) Determine if the quadrilateral must be a parallelogram. Justify your answer.

Example 5) Determine if the quadrilateral must be a parallelogram. Justify your answer.

Example 6) Determine if the quadrilateral must be a parallelogram. Justify your answer.

Example 7) Determine if each quadrilateral must be a parallelogram. Justify your answer.

Example 8) Determine if the set of vertices below form a parallelogram. J(–1, –6), K(–4, –1), L(4, 5), M(7, 0).

Example Determine if the set of vertices below form a parallelogram. (1, 1) (6, 3) (8, -2) (3, -4)

Example Determine if the set o vertices below form a parallelogram. (-5, -1) (0, 9) (11, 11) (5, 1)