Final answer:
Corresponding angles in similar shapes are equal, not proportional. A vector can form a right angle triangle with its components, allowing use of the Pythagorean theorem. The amplitude of a wave is affected by another wave's amplitude when they are aligned, regardless of their line of propagation.
Step-by-step explanation:
The statement "Corresponding angles of similar shapes must be proportional" is actually false. In similar shapes, corresponding angles are equal, and it is the corresponding sides that are proportional, not the angles.
In vector mathematics, a vector can certainly form the shape of a right angle triangle with its x and y components, and this is why we can use the Pythagorean theorem to calculate the length of the resultant vector when the two vectors are at right angles to each other.
For waveform interference, it is true that the amplitude of one wave is affected by the amplitude of another wave when they are in phase (or precisely aligned). The amplitudes of waves add up constructively or destructively depending on their relative phases and alignment, not only if they are propagating in the same line.