Given a dilation with the origin o (0,0), by observation determine the scale favor “k”. do, k = (5,0) —> (15,0) what is the scale factor k

3

Step-by-step explanation:

Since there is no increase in height, we will look at the horizontal distance.

We can compare the distance from (0,0) to (5,0) and (15,0)

Distance from (0,0) to (5,0) = 5 units

(0,0) to (15,0) = 15 units

So, k is the ratio of the new distance over the original: k = 15/5 --> k = 3

-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.