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 overline LN is the same as midpoint of overline MP . B. Show that LN=MP. C. Show that LM=NP and MN=LP. D. Show that slope of overline LN slope of overline MP=-1.

Answer 1

Options A, B, and C shows that quadrilateral LMNP on the coordinate plane is a parallelogram

Analysis of the options

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

This condition is true for parallelograms, as opposite sides of a parallelogram have the same midpoint.

B. Show that LN = MP

This condition is true for parallelograms. Opposite sides of a parallelogram are equal in length.

C. Show that LM = NP and MN=LP

This condition is true for parallelograms. Opposite sides of a parallelogram are equal in length.

D. Show that slope of overline LN slope of overline MP = -1

This condition is not generally true for parallelograms. The slopes of opposite sides of a parallelogram are negative reciprocals of each other, not necessarily -1.