Select the correct answer.
which set of vertices forms a parallelogram?
a.
a(2, 4), b(3, 3), c(6, 4), d(5, 6)
b.
a(-1, 1), b(2, 2), c(5, 1), d(4, 1)
c.
a(-5, -2), b(-3, 3), c(3, 5), d(1, 0)
d.
a(-1, 2), b(1, 3), c(5, 3), d(1, 1)

OPTION C.

Step-by-step explanation:

A parallelogram is defined as a quadrilateral which has two pairs of parallel sides.

Attached is shown in the parallelogram obtained by plotting the vertices provided in Option C.

If that figure is a parallelogram, then:

Let's check this:

Therefore, the set of vertices that forms a parallelogram is:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

answer: y=4000x+14000

step-by-step explanation: