According to a pencil company's advertising campaign, 2 out of 3 students prefer the company's pencils to their competitor's pencils. A representative of the company went to a high school with 1479 students for a Q & A session, and one of the students asked, "If this is true, in this high school, how many more students are there who prefer your pencils than students who prefer your competitor's pencils?" Help the company's representative come up with an answer. Assume that the company's claim is true. Part I: How many of the students in the high school prefer the company's pencils?

Part II: Out of 3 students, how many prefer the pencils of the company's competitor?

Part III: How many of the students in the high school prefer the pencils of the company's competitor?

Part IV: In the high school, how many more students are there who prefer the company's pencils than students who prefer their competitor's pencils?

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parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

∠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.