Find the distance between the two points. (4,3)
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 89 will go in the box

This means the exact distance between the two given points is which approximates to roughly 9.4339811

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Explanation:

To get that answer, we can apply the distance formula

(x1,y1) = (-1,-5) is the first point

(x2,y2) = (4,3) is the second point

Plug the coordinates into the distance formula

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Alternative Method:

You could also form a right triangle by adding the point (4, -5). The horizontal leg goes from (-1,-5) to (4,-5) which is a span of 5 units. The vertical leg goes from (4,-5) to (4,3) which is a span of 8 units. The hypotenuse is from (-1,-5) to (4,3) which is the distance we want to find.

After forming the triangle and determining the leg lengths, use the pythagorean theorem and you should get as the length of the hypotenuse. As you can probably guess, the distance formula is effectively a slight rephrasing the pythagorean theorem.

-232

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.