6-3 Proving That a Quadrilateral Is a Parallelogram

Objective

To determine whether a quadrilateral is a parallelogram

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In the Solve It, you used angle properties to show that lines are parallel. In this lesson, you will apply the same properties to show that a quadrilateral is a parallelogram.

Essential Understanding You can decide whether a quadrilateral is a parallelogram if its sides, angles, and diagonals have certain properties.

In Lesson 6-2, you learned theorems about the properties of parallelograms. In this lesson, you will learn the converses of those theorems. That is, if a quadrilateral has certain properties, then it must be a parallelogram. Theorem 6-8 is the converse of Theorem 6-3.

Theorems 6-9 and 6-10 are the converses of Theorems 6-4 and 6-5, respectively. They use angle relationships to conclude that a quadrilateral is a parallelogram.

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