Suppose that a given quadrilateral is a kite with no right angles. Which of the following is possible?
A) The quadrilateral is a trapezoid. B) The quadrilateral is a rhombus.
C) The quadrilateral has congruent diagonals. D) None of the above
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To determine which of the given options is possible for a kite with no right angles, we need to understand the properties of each option.
A) The quadrilateral is a trapezoid: A trapezoid is a quadrilateral with exactly one pair of parallel sides. A kite does not have parallel sides, so it cannot be a trapezoid. Therefore, option A is NOT possible.
B) The quadrilateral is a rhombus: A rhombus is a quadrilateral with all sides congruent. A kite does have two pairs of congruent adjacent sides, but the other two sides are not congruent. Therefore, option B is NOT possible.
C) The quadrilateral has congruent diagonals: The diagonals of a kite bisect each other at a right angle, but they are not necessarily congruent. Therefore, option C is NOT possible.
D) None of the above: Since options A, B, and C are all NOT possible, the correct answer is option D) None of the above.
In summary, for a given kite with no right angles, none of the given options (A, B, or C) are possible.