Question

geometry b is (bva) 25-26 / semester exam

1. which of the following statements is true about using a quadrilateral to construct a parallelogram?

the sides of the quadrilateral can be any length and the angles can be any measure.
all sides of the quadrilateral must be congruent and all angles must be congruent.
opposite sides of the quadrilateral must be parallel and opposite angles must be congruent.
adjacent sides of the quadrilateral must be perpendicular and adjacent angles must be congruent.

Explanation:

To determine the true statement about constructing a parallelogram from a quadrilateral, we recall the definition of a parallelogram: a quadrilateral with opposite sides parallel and opposite angles congruent. Let's analyze each option:

1. "The sides... any length, angles any measure": False. A general quadrilateral (e.g., a trapezoid with only one pair of parallel sides) does not satisfy the parallelogram definition.
2. "All sides congruent, all angles congruent": False. This describes a rhombus (or square), but a parallelogram only requires opposite sides/angles to be congruent (not all sides/angles).
3. "Opposite sides parallel, opposite angles congruent": True. This matches the definition of a parallelogram.
4. "Adjacent sides perpendicular, adjacent angles congruent": False. This describes a rectangle (or square), but a parallelogram does not require adjacent sides to be perpendicular (only that opposite sides are parallel).

Answer:

C. Opposite sides of the quadrilateral must be parallel and opposite angles must be congruent.