Use the points (1, -3) and (5, 9) for the following problems. a. determine the slope between the two points above using the slope formula. show all work. b. use the slope from part (a) and one point from above to write the equation in point-slope form.

Slope =3

process--

=3

Point-slope form is 3x-y-6=0 (using the first set of points, (1,-3) )

process--

y-9=3(x-5)

y-9=3x-15

y=3x-15+9

y=3x-6

3x-y-6=0

∠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.