Final answer:
It's true that a line segment being a diameter of a circle means its endpoints are on the circle. Using the Pythagorean theorem for the length of a resultant vector of two perpendicular vectors and a vector forming the shape of a right-angle triangle with its components are also true.
Step-by-step explanation:
The conditional statement 'If a line segment is a diameter of a circle, then its endpoints are on that circle' is indeed true. A diameter of a circle is defined as a line segment that passes through the center of the circle and whose endpoints lie on the circle. Therefore, by definition, the endpoints of a diameter must be on the circle.
When discussing the use of the Pythagorean theorem in calculating the length of a resultant vector from the addition of two vectors at right angles to each other, this is also true. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (resultant vector) is equal to the sum of the squares of the lengths of the other two sides (the vectors). This makes it applicable in this situation.
For the concept of a vector forming a right-angle triangle with its x and y components, this is true as well. Vectors have both magnitude and direction, and in a two-dimensional plane, a vector can be decomposed into its orthogonal x and y components, which can be represented as the legs of a right-angled triangle, with the vector itself representing the hypotenuse.