Question

question 14 (multiple choice worth 1 points) (04.01 lc) which statement explains how you could use coordinate geometry to prove that quadrilateral abcd is a rectangle? prove that segments ad and ab are congruent and parallel. prove that opposite sides are congruent and that the slopes of consecutive sides are equal. prove that segments bc and cd are congruent and parallel. prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals.

Explanation:

To prove a quadrilateral is a rectangle, we can show opposite sides are congruent (using distance formula) and consecutive sides are perpendicular (slopes are negative reciprocals). The fourth option says "Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals", which matches the rectangle properties (opposite sides equal, consecutive sides perpendicular). Other options: first two focus on non - rectangle - specific pairs or wrong slope relations, third has wrong slope description.

Answer:

The fourth option: Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals.