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. lp ⊥ pn

Explanation:

Step1: Recall rectangle properties

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

Step2: Analyze each option

For the first option, just knowing the lengths of two adjacent sides ($\sqrt{45}$ and $\sqrt{5}$) of a parallelogram does not prove it is a rectangle.
For the second option, the slope of two opposite sides being equal just shows they are parallel (which is a property of a parallelogram already), not that it is a rectangle.
For the third option, if $LP\perp PN$, then one of the angles of the parallelogram $LMNP$ is a right - angle. Since $LMNP$ is a parallelogram, if one angle is a right - angle, then all angles are right - angles and it is a rectangle.

Answer:

$LP\perp PN$