Answer:
A. Consecutive sides have opposite reciprocal slopes
Step-by-step explanation:
A rectangle is a special case of parallelogram, in which the diagonals bisect each other and are the same length, and all angles are right angles. In order to prove a quadrilateral is a rectangle, it can be shown to be a parallelogram, but one or the other of these additional characteristics must be proven.
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A. Consecutive sides have opposite reciprocal slopes
Sides with opposite reciprocal slopes will be perpendicular. That is, the angle between them will be a right angle. If all pairs of consecutive sides meet at right angles, the figure must be a rectangle.
B. All sides are congruent
A <em>rhombus</em> is a quadrilateral in which all sides are congruent. It will only be a rectangle if the diagonals are the same length, or, equivalently, adjacent sides meet at right angles.
C. Opposite sides are parallel
A <em>parallelogram</em> will have opposite sides parallel. It will only be a rectangle if the diagonals are the same length, and/or adjacent sides meet at right angles.
D. Consecutive sides are congruent, opposite sides are not.
This seems a contradiction, as opposite sides are consecutive to the same side. (For example, sides AB and CD are both consecutive to side BC.) If we take this to mean that there are two pairs of consecutive congruent sides, then the figure may be a <em>kite</em>, but isn't necessarily a rectangle unless the other conditions are met.
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<em>Additional comment</em>
If sides are horizontal and vertical, the slope of the vertical sides is "undefined." It cannot be shown to be the opposite reciprocal of the slope of the horizontal sides.
