When Lila conducted an experiment on citywide pond water, all of her samples came from the pond in her uncle's backyard. Explain her error.

Her area of study is too narrow. There are other sources of water in the city that she is not considering. So her sample is too biased leaning toward the Uncle's pond water, and that leaves out every other source. We say that the Uncle's source of water is over-represented while the other sources are completely under-represented.

Let's put it this way: We have a hypothetical city that has 100 acres of pond water either in or surrounding the city limits. If the Uncle's pond only represents 1% of this, then she's ignoring the other 99% of the ponds.

What Lila needs to do to to fix this error is to draw up a map of each major pond and mark those ponds with numbers 001,002,...998,999. In this example, there are 999 ponds. Then she needs to either use a random number table or computer software to help randomly generate values to help select the ponds. Doing so will ensure that she spans a good portion of the city and not stay focused on just the narrow area of her Uncle's backyard.

The reason why she needs to enlarge her area of study is because the results of her Uncle's pond study may lead to the wrong conclusion of the city overall. Let's say his pond is contaminated somehow, and it's only his pond that's the unfortunate one. She would likely see the pond is contaminated and conclude that the whole city's water is ruined as well, which isn't the case. Or we could have nearly the entire city's pond water in trouble, but her Uncle's pond is one of the lucky ponds not to get contaminated. We can see that Lila would likely conclude that no action needs to be taken to clean up the city's water sources, which is also not the case.

If Lila only cared about her Uncle's pond, then that pond (and perhaps immediate close surrounding area) would be her population of study. However, her study is about citywide pond water which is why she needs to extend to other places in the city or in the outer surrounding areas.

∠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.