Question

Which of the following would show that quadrilateral LMNP on the coordinate plane is a parallelogram? Select all that apply. A. Show that midpoint of LN is the same as midpoint of MP B. Show that LN = MP. C. Show that LM = NP and MN = LP. D. Show that (slope of LN (slope of MP )=-1.

Answer 1

Options A and D are the ones that would help show that quadrilateral LMNP is a parallelogram.

To show that quadrilateral LMNP on the coordinate plane is a parallelogram, you can use the following criteria:

A. Show that midpoint of LN is the same as midpoint of MP.

This is a property of parallelograms. If the midpoints of one pair of opposite sides are the same, it indicates a parallelogram.

B. Show that LN = MP.

This alone does not necessarily prove that LMNP is a parallelogram. Equal lengths of opposite sides are a property of parallelograms, but it is not sufficient on its own.

C. Show that LM = NP and MN = LP.

This alone does not necessarily prove that LMNP is a parallelogram. Equal lengths of pairs of opposite sides are a property of parallelograms, but it is not sufficient on its own.

D. Show that the slope of LN multiplied by the slope of MP is equal to -1.

This is a property of parallelograms. If the product of the slopes of one pair of opposite sides is -1, it indicates a parallelogram.

Therefore, options A and D are the ones that would help show that quadrilateral LMNP is a parallelogram.