In any quadrilateral, the properties of sides, angles, and diagonals can vary widely. However, the statement given is that the quadrilateral has congruent opposite angles. Let's analyze each of the provided statements in the context of a quadrilateral with congruent opposite angles:
1. All sides are congruent:
This statement is not necessarily true. While a square or a rectangle does have congruent opposite angles and congruent sides, a kite or a dart (also known as an arrowhead or a chevron) can have congruent opposite angles without all sides being congruent.
2. The diagonals are congruent:
Again, this statement is not necessarily always true. While a rectangle has congruent opposite angles and congruent diagonals, a kite may have congruent opposite angles but typically does not have congruent diagonals.
3. Consecutive angles are congruent:
This statement is also not necessarily true. A rectangle or a square does have congruent consecutive angles since all angles are 90 degrees, but other quadrilaterals like a rhombus or a kite have congruent opposite angles without the consecutive angles necessarily being congruent.
4. If one angle is 90°, then all angles are 90°:
This statement is incorrect. Having one 90-degree angle in a quadrilateral does not imply that all angles are 90 degrees. Only in the case of a rectangle or square are all angles congruent, and they are all right angles. However, there are other quadrilaterals with one right angle and congruent opposite angles that are not rectangles or squares (e.g., a right kite).
Based on the above analysis, none of the provided statements are always true for a quadrilateral with congruent opposite angles. Therefore, the correct answer to the question is that none of the given statements about William's quadrilateral is always true.
