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Proving Parallelograms: Tests and Examples

Explore methods to prove if a quadrilateral is a parallelogram using tests like parallel sides, congruent angles, and diagonals. Practice identifying and graphing parallelograms with examples and homework worksheets.

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Proving Parallelograms: Tests and Examples

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  1. Geometry 6.3 Tests for Parallelograms

  2. Proving a Quadrilateral is a Parallelogram • Only one of the following needs to be shown: • 1) Show that both pairs of opposite sides are parallel. • 2) Both pairs of opposite sides are congruent. • 3) Both pairs of opposite angles are congruent. • 4) The diagonals bisect each other. • 5) A pair of opposite sides is both parallel and congruent.

  3. Example 1 • Determine if the following quadrilaterals are parallelograms, if yes explain.

  4. Example 2 • Find x and y so that the quadrilateral is a parallelogram.

  5. Example 3 • Graph quadrilateral QRST with vertices Q(-1,3), R(3,1), S(2, -3), and T(-2,-1). Determine if it is a parallelogram using the slope formula.

  6. Homework • Worksheet

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