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 parallelogram is a rectangle if one of its angles is a right - angle. In a coordinate plane, perpendicular lines have slopes that are negative reciprocals of each other.

Step2: Analyze each option

• Option 1: Just knowing the lengths of two adjacent sides does not prove it's a rectangle.
• Option 2: Knowing the slope of two parallel sides does not prove it's a rectangle.
• Option 3: \(LM\) and \(PN\) are opposite sides in a parallelogram. Parallel sides in a parallelogram are not perpendicular in general.
• Option 4: \(LP\) and \(PN\) are adjacent sides. If \(LP\perp PN\), then one of the angles of the parallelogram \(LMNP\) is a right - angle, and thus the parallelogram is a rectangle.

Answer:

LP ⊥ PN