Testing for Parallelograms
Overview
Lesson 59 listed the properties of a parallelogram; this lesson turns them around. Each property becomes a test: if a quadrilateral passes any one of the six tests in this lesson, it is guaranteed to be a parallelogram. You will apply the tests to figures described by their sides, angles, and diagonals, and find the values of x and y that force a quadrilateral to pass a test.
Vocabulary
- Parallelogram
- A quadrilateral with both pairs of opposite sides parallel.
- Bisect
- To divide a segment or an angle into two congruent parts.
- Sufficient Condition
- A condition that is enough, by itself, to guarantee a conclusion. Each test in this lesson is a sufficient condition for a quadrilateral to be a parallelogram.
Main Ideas
- A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (the definition).
- A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.
- A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.
- A quadrilateral is a parallelogram if consecutive angles are supplementary in both directions.
- A quadrilateral is a parallelogram if the diagonals bisect each other.
- A quadrilateral is a parallelogram if one pair of opposite sides is both parallel and congruent.
Lesson Notes
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Lesson Video
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Practice Problems
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Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.