Geometry: Polygons and Parallelograms

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What are the 5 ways to prove that a given quadrilateral is a parallelogram?

The 5 ways to prove that a given quadrilateral is a parallelogram are: opposite sides are parallel, opposite angles are congruent, diagonals bisect each other, consecutive angles are supplementary, and one pair of opposite sides and angles are congruent.

How can you differentiate between the definition of a parallelogram and the theorems about properties of a parallelogram?

The definition of a parallelogram states that it is a quadrilateral with opposite sides parallel, while the theorems about properties of a parallelogram include the properties such as opposite angles being congruent and consecutive angles being supplementary.

What is the relationship between the interior and exterior angles of a convex polygon?

The sum of the interior angles of a convex polygon is equal to 180*(n-2) degrees, where n is the number of sides. The sum of the exterior angles of a convex polygon is always 360 degrees.

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