Final answer:
The answer to the student's question is True; in similar triangles, the corresponding angles are equal. This fact is essential in the principles of geometry and trigonometry, which are also used in physics for vector resolution and vector components.
Step-by-step explanation:
The student's question refers to the properties of similar triangles. The statement is True; in similar triangles, the corresponding angles are equal by definition. This is a foundational concept in geometry, a branch of mathematics. When two triangles are similar, the angles that match are called corresponding angles, and they are congruent, which means they have the same measure.
Several other points mentioned revolve around the use of geometry and trigonometry in different scenarios. For example, the Pythagorean theorem can indeed be used to calculate the length of the resultant vector when two vectors are at right angles to each other because the situation forms a right-angled triangle. Vectors can be split into their x and y components, creating right-angled triangles, which is why trigonometry is often used to resolve vector problems in physics.