Opposite Sides of a Parallelogram

In a parallelogram, the opposite sides are parallel and congruent. This means that they have the same length.

Definition of a Parallelogram

A parallelogram is a four-sided polygon with opposite sides that are parallel. It has two pairs of opposite sides that are congruent. The opposite sides of a parallelogram are also called the "base" and the "height" of the parallelogram.

Properties of a Parallelogram

1. Opposite Sides: The opposite sides of a parallelogram are parallel and congruent. This means that they have the same length.

2. Opposite Angles: The opposite angles of a parallelogram are congruent. This means that they have the same measure.

3. Consecutive Angles: The consecutive angles of a parallelogram are supplementary. This means that the sum of two consecutive angles is 180 degrees.

4. Diagonals: The diagonals of a parallelogram bisect each other. This means that they divide each other into two equal parts.

Explanation of the Answer

The question states that the opposite sides of a parallelogram are of ________ length. The correct answer is option 'C', which states that the opposite sides are equal in length.

This answer is based on the definition and properties of a parallelogram. Since a parallelogram has opposite sides that are parallel and congruent, it follows that the opposite sides have the same length. This is a fundamental characteristic of parallelograms.

Therefore, when considering the length of the sides of a parallelogram, we can conclude that the opposite sides are equal. This property distinguishes parallelograms from other quadrilaterals, such as rectangles or rhombuses, which have different side lengths.

In summary, the opposite sides of a parallelogram are of equal length. This property is a defining characteristic of parallelograms and is true for all parallelograms.