Use the list of five irrational below to answer the questions
square root of 2, square root of 6, square root of 12, square root of 18, and square root of 24.
part a. choose two numbers whose product is rational. explain.
part b. choose two numbers whose product is irrational. explain.

Step-by-step explanation:

A: The root will be rational if the product of the numbers under the radicals is a perfect square. For this part, there are a couple of choices.

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B: The root will be irrational if the product of the numbers under the radicals is not a perfect square. For this part, there are many choices.

∠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.

answer: about 22.67

step-by-step explanation: