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If angle WZY = 90°, must WXYZ be a rectangle?

A. True
B. False

Answer :

Final answer:

The statement is false; angle WZY being 90° does not guarantee that WXYZ is a rectangle. Quadrilaterals require all angles to be 90° to be classified as rectangles, which is not specified in the given conditions.

Explanation:

If angle WZY = 90°, it does not necessarily mean that WXYZ must be a rectangle. For WXYZ to be a rectangle, all interior angles must be right angles (90°) and opposite sides must be parallel and of equal length. A quadrilateral with just one right angle could be a trapezoid, a kite, or another irregular quadrilateral, which does not fulfill the criteria of a rectangle. Therefore, the statement is False.

In reference to vectors and their components:

  • A vector can indeed form the shape of a right angle triangle with its x and y components, which is True.
  • 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, which is also True.
  • The x-component of a vector with a specific angle will be greater than its y-component when 0° < angle < 45° because in this range, the cosine value (which is related to the x-component) is greater than the sine value (related to the y-component).

If only the angles of two vectors are known, we cannot find the angle of their resultant addition vector without additional information, such as the magnitudes of the vectors, which makes the statement False.

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Rewritten by : Barada