Final answer:
The statement regarding opposite angles in a quadrilateral being congruent to form a parallelogram is true. The Pythagorean theorem can be used for perpendicular vectors to find the resultant vector, and waves of different frequencies can superimpose.
Step-by-step explanation:
If opposite angles of quadrilateral PQRS are congruent, it is true that it is a parallelogram. This statement aligns with one of the key properties of a parallelogram where both pairs of opposite angles are equal.
True or False: We can use the Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other. True. When two vectors are perpendicular, they form a right-angled triangle, and the Pythagorean theorem can be used to find the magnitude of the resultant vector.
A vector can indeed form the shape of a right-angle triangle with its x and y components. This is true and fundamental to vector decomposition. When two vectors are added, and if they are perpendicular, they form a 90° angle between each other.
For the GRASP CHECK, it is false. If only the angles of two vectors are known, we cannot find the angle of their resultant addition vector without additional information. Regarding the magnitude and direction of the resultant vector, it is true that we can find these if we know the angles of two vectors and the magnitude of at least one of them.
It is also true that waves can superimpose if their frequencies are different. This principle is pivotal in understanding wave interference. The amplitude of one wave is affected by the amplitude of another wave only when they are precisely aligned, which is true. This alignment leads to constructive or destructive interference depending on the phase relationship between the waves.