Question

What additional information would prove that lmnp is a rectangle? the length of lm is startroot 45 endroot and the length of mn is startroot 5 endroot. the slope of lp and mn is –2. lm ∥ pn lp ⊥ pn

Answer 1

Rectangles are recognized to have the same qualities as parallelograms. The alternative with the additional information would demonstrate that LMNP is a rectangle is LP ⊥ PN.

What are rectangles?

• A rectangle is a quadrilateral with four right angles in Euclidean plane geometry.
• It can also be classified as an equiangular quadrilateral because all of its angles are equal, or a parallelogram with a right angle.
• A square is a rectangle with four equal-length sides.

What to know about parallelogram and rectangle:

• They both have two sorts of parallel sides as well as two pairs of opposite sides that are said to be congruent. All of the properties of a parallelogram are said to be shared by a rectangle.

• This results in a rectangle and, invariably, a parallelogram.
• However, a parallelogram is not generally referred to as a rectangle.

• Option d, LP ⊥ PN as the supplementary information, would demonstrate that LMNP is a rectangle.

Therefore, rectangles are recognized to have the same qualities as parallelograms. The alternative with the additional information would demonstrate that LMNP is a rectangle is LP ⊥ PN.

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The correct question is given below:
LMNP is a parallelogram.

What additional information would prove that LMNP is a rectangle?

A. The length of LM is √45 and the length of MN is √5.

B. The slope of LP and MN is –2.

C. LM ∥ PN

D. LP ⊥ PN