Unit 7 of the geometry curriculum focuses on Polygons and Quadrilaterals, and is a key part of learning the fundamentals of geometry. In this unit, students will learn the properties of various quadrilaterals, such as squares, rectangles, rhombuses, and parallelograms. Homework 2 of this unit covers parallelograms, which are quadrilaterals that have two pairs of parallel sides. Understanding the properties of parallelograms is important for further understanding of geometry.

## Definition of a Parallelogram

A parallelogram is a four-sided shape that has two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to one another, and the angles of a parallelogram are all equal. As a result, a parallelogram is a quadrilateral with opposite sides that are equal in length and parallel to one another.

## Properties of a Parallelogram

A parallelogram has four important properties: opposite sides are equal in length and parallel to one another, opposite angles are equal, the diagonals bisect each other, and the sum of the interior angles equals 360 degrees. These properties can be used to prove that a given quadrilateral is a parallelogram, as well as to find missing information about the shape. In addition, it is important to note that the opposite sides of a parallelogram are not necessarily congruent.

## How to Prove a Quadrilateral is a Parallelogram

There are a few different methods for proving that a given quadrilateral is a parallelogram. The most common method is to use the properties of a parallelogram to prove that opposite sides are equal in length and parallel to one another. If these two conditions can be proven true, then the given quadrilateral is a parallelogram. Other methods for proving a quadrilateral is a parallelogram include using properties such as opposite angles being equal, the diagonals bisecting each other, and the sum of the interior angles equaling 360 degrees.

## Conclusion

Unit 7 of the geometry curriculum focuses on polygons and quadrilaterals, and homework 2 covers parallelograms. A parallelogram is a quadrilateral with two pairs of parallel sides that are equal in length. The properties of a parallelogram can be used to prove that a given quadrilateral is a parallelogram, as well as to find missing information about the shape. Understanding the properties of parallelograms is an important part of learning the fundamentals of geometry.

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