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Geometry. 6.3 Tests for Parallelograms. 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.

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Geometry

Geometry

6.3

Tests for Parallelograms


Proving a quadrilateral is a parallelogram

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.


Example 1

Example 1

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


Example 2

Example 2

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


Example 3

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.


Homework

Homework

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