Final answer:
The given statement "Lie on the same side of a transversal in corresponding positions" is True because the Pythagorean theorem can be used to calculate the length of the resultant vector obtained from the addition of two vectors that are at right angles to each other. The correct option is a.
Step-by-step explanation:
The statement is True. The Pythagorean theorem can be used to calculate the length of the resultant vector obtained from the addition of two vectors that are at right angles to each other.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the case of two vectors at right angles, their magnitudes can be represented as the lengths of the perpendicular sides of a right triangle, and the magnitude of the resultant vector can be calculated using the Pythagorean theorem.
For example, if vector A has a magnitude of 3 units and vector B has a magnitude of 4 units, and they are at right angles to each other, the magnitude of their resultant vector C can be calculated as follows:
C =√(A² + B²) = √(3² + 4²) = √(9 + 16) = √(25) = 5 units
Hence, a is the correct option.