Leo wants to determine the average number of texts middle school students send in a day. Since all middle school students are enrolled in history, he randomly surveyed 4 students from each of Mr. Barnes’s eighth-grade history classes. Ms. Lopez and Mrs. Frank also teach eighth-grade history. What should Leo do to ensure his sample is representative of all middle school students? He should take the sample as is because he randomly surveyed students in each of Mr. Barnes’s classes. He should also take a sample from Ms. Lopez’s and Mrs. Frank’s classes so that each student has the same chance of being chosen. He should also take a sample from each of the other history classes in all of the other grades in the middle school. He should survey all the students in all the history classes to make sure he collects enough data.

∠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.