suppose that a given quadrilateral is a kite with no right angles. which of the following is possible
A: the quadrilateral is a rhombus
B: the quadrilateral has congruent diagnols
C: the quadrilateral is a trapezoid
D: None
Draw the various choices and see.
For example draw a trapezoid.
Can you do it so it has no right angles?(of course)
Can it have congruent diagonals (go ahead draw it)
Could it be a rhombus?
ANGLE A= angle d=180
angle b +angle d =180
angle a=angl d
2angled =180
angle d =90
To determine which of the options is possible, let's analyze each statement:
A: The quadrilateral is a rhombus.
A rhombus is a quadrilateral with four congruent sides. A kite, on the other hand, is a quadrilateral with two pairs of adjacent sides that are congruent. Since a kite does not have four congruent sides, it cannot be a rhombus. Therefore, option A is not possible.
B: The quadrilateral has congruent diagonals.
The diagonals of a kite are always perpendicular bisectors of each other. Since the diagonals in a kite are not congruent, this option is not possible.
C: The quadrilateral is a trapezoid.
A trapezoid is a quadrilateral with at least one pair of parallel sides. Since a kite does not have any parallel sides, it cannot be a trapezoid. Therefore, option C is not possible.
D: None.
Based on our analysis, options A, B, and C are not possible, which means the correct answer is D: None.
In summary, for a given quadrilateral to be a kite with no right angles, it cannot be a rhombus, the diagonals cannot be congruent, and it cannot be a trapezoid.