Question

which of the following is true for a trapezoid? its diagonals always bisect each other. it has two pairs of congruent sides. it does not have two pairs of congruent sides. its opposite angles are congruent.

Explanation:

1. Analyze the first option: Diagonals bisecting each other is a property of parallelograms (like rectangles, rhombuses, etc.), not all trapezoids. A trapezoid has only one pair of parallel sides, and in general, its diagonals do not bisect each other. So this is false.
2. Analyze the second option: A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. Most trapezoids do not have two pairs of congruent sides. Only special trapezoids like isosceles trapezoids have the non - parallel sides (legs) congruent, but not two pairs of congruent sides in general. So this is false.
3. Analyze the third option: As explained above, a general trapezoid (with only one pair of parallel sides) does not have two pairs of congruent sides. Even an isosceles trapezoid has only one pair of congruent sides (the legs), not two pairs. So this statement is true.
4. Analyze the fourth option: Opposite angles being congruent is a property of parallelograms. In a trapezoid, only in isosceles trapezoids are the base angles congruent, but not all opposite angles. So this is false.

Answer:

C. It does not have two pairs of congruent sides. (Here we assume the options are labeled A, B, C, D in order. If the original options have different labels, adjust accordingly. Since the original image shows the options in the order: first option, second, third, fourth, we can say the third option "It does not have two pairs of congruent sides" is correct.)