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Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: points A, B, C, and D
Conjecture: A, B, C, and D are coplanar.

A. False; the four points do not have to be in a straight line.
B. False; two points are always coplanar but four are not.
C. True
D. False; three points are always coplanar but four are not.

The correct answers are B and D.

A is false because, even though it's true that 4 points are not necessarily on the same line, it is not required that they are collinear in order for them to be coplanar.

B is true: two points always lie on the same line (and thus also in infinite same planes), but four points are not always coplanar

C is false. As a counterexample pick the four points (0,0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1).

D is true: two points are always on the same line, three points always lie in a common plane, but 4 points are not necessarily coplanar.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

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