Question

If one pair of opposite sides of a quadrilateral are congruent, then the

quadrilateral is a parallelogram.
O A. True
O B. False

Answer 1

The statement about the quadrilateral being a parallelogram if one pair of opposite sides are congruent is False. With regard to vectors, the Pythagorean theorem is used for calculating the resultant vector at right angles, vectors can form right-angle triangles with their components, and displacement is the same regardless of the order of movement.

Step-by-step explanation:

If one pair of opposite sides of a quadrilateral are congruent, then the statement that the quadrilateral is a parallelogram is False. While having a pair of congruent opposite sides is a property of a parallelogram, it is not sufficient on its own to definitively classify a quadrilateral as a parallelogram. Additional properties such as both pairs of opposite sides being congruent, the diagonals bisecting each other, or one pair of opposite sides being both congruent and parallel are needed to conclude that a quadrilateral is indeed a parallelogram.

Regarding the concepts related to vectors in physics:

1. The Pythagorean theorem can be used to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other. This is True.
2. A vector can indeed form the shape of a right-angle triangle with its x and y components, making the statement True.
3. Two vectors that have identical directions are said to be parallel vectors. They are considered equal if they have the same magnitude, A = B.
4. Vectors that are perpendicular to each other are known as orthogonal vectors.
5. It is False that the displacement of a person who walks 2 blocks east and 5 blocks north is more than the displacement of a person who walks the same distance but in a different order.