Construction of a Parallelogram

To construct a parallelogram, we need to know two adjacent sides and one angle. Let's understand why this is the correct answer.

Parallelogram Properties:
1. Opposite sides of a parallelogram are parallel.
2. Opposite sides of a parallelogram are congruent (equal in length).
3. Opposite angles of a parallelogram are congruent.
4. Adjacent angles of a parallelogram are supplementary (add up to 180 degrees).
5. Diagonals of a parallelogram bisect each other.

Constructing a Parallelogram:
To construct a parallelogram, we start with two adjacent sides and one angle.

1. Draw the given two adjacent sides AB and AD using a ruler. Label the endpoints as A, B, C, and D.
2. From point A, construct an angle equal to the given angle. Label the vertex of this angle as E.
3. Using a compass, measure the length of one of the given sides and place the compass at point B. Draw an arc to intersect the angle bisector at F.
4. With the same compass setting, place the compass at point D and draw an arc to intersect the angle bisector at G.
5. Draw a line from point F to point D and extend it.
6. Draw a line from point G to point B and extend it.
7. The intersection of the extended lines from steps 5 and 6 will give us point C.
8. Connect points A, B, C, and D to complete the parallelogram ABCD.

Explanation:
By constructing a parallelogram using two adjacent sides and one angle, we ensure that the opposite sides are parallel and congruent. The given angle helps us determine the direction and shape of the parallelogram. The congruent opposite angles and supplementary adjacent angles are automatically satisfied due to the nature of parallelograms.

If we were given only the length of the parallel sides, we would not be able to determine the shape or the angles of the parallelogram. Similarly, if we were given only the measure of the angles, we would not have enough information to determine the length of the sides or the shape of the parallelogram.

Hence, the correct answer is option 'C' - Two adjacent sides and one angle.