Question

lmnp is a parallelogram. what additional information would prove that lmnp is a rectangle? the length of lm is √45 and the length of mn is √5. the slope of lp and mn is -2. lm // pn lp ⊥ pn

Explanation:

Step1: Recall rectangle properties

A rectangle is a parallelogram with one - right angle. In a coordinate - plane, perpendicular lines have slopes whose product is - 1. In a parallelogram, if adjacent sides are perpendicular, then it is a rectangle.

Step2: Analyze each option

• Option 1: Knowing the lengths of two sides (\(\sqrt{45}\) and \(\sqrt{5}\)) does not prove that the angles are right - angles.
• Option 2: The fact that two non - adjacent sides have the same slope just shows they are parallel, not that the parallelogram is a rectangle.
• Option 3: \(\overline{LM}\parallel\overline{PN}\) is a property of a parallelogram, not a property that makes it a rectangle.
• Option 4: If \(\overline{LP}\perp\overline{PN}\), since \(LMNP\) is a parallelogram, having one right - angle in a parallelogram makes all angles right - angles (properties of parallelograms), so it is a rectangle.

Answer:

D. \(\overline{LP}\perp\overline{PN}\)