Download Section 6.3

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.
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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.
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry