Line segment AC and BD are parallel. What are the new endpoints of the line segments AC and BD if the parallel lines are reflected across the x-axis? A. A'(-2, 5) C'(5, 1) and B'(-2, -4) D'(5, 0)
B. A'(-5, -2) C'(-1, 5) and B'(-4, -2) D'(0, 5)
C. A'(2, -5) C'(-5, -1) and B'(2, -4) D'(-5, 0)
D. A'(5, 2) C'(1, -5) and B'(4, 2) D'(0, -5)

∠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.