Astandard letter-sized piece of paper has a length and width of 8.5 inches by 11 inches.
b. if the paper were folded completely in half, what would be the area of the resulting rectangle?

Area of the resulting rectangle = 23.375 inch²

Step-by-step explanation:

After 1 fold width or length reduces to half.

Area = Length x width

So after 1 fold area will reduce to half.

So we have

Initial area = 8.5 x 11 = 93.5 inch²

Here the paper were folded completely in half, length is reduced to half and width reduced to half, that is

Number of folds = 2

Area after 2 folds = 23.375 inch²

Area of the resulting rectangle = 23.375 inch²

d

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.