What is the exact distance between point e and point f

The answer to your question is: d = √73  

Step-by-step explanation:

data

Point E (-3, 4)

Point F (5, 1)

Formula

d = √((x2-x1)² + (y2-y1)²)

d = √(5-(-3))² + (1-4)²)          substitution

d= √ (5+3)² + (-3)²               simplify

d= √ 8² + -3²

d = √ 64 + 9

d = √73                               result

answer: slight chance that it will happen

step-by-step explanation:

∠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.