Write one inequality statement to show the relationship among the following shoe sizes: 10 1/2, 8, and 9.
a. from least to greatest:
b. from greatest to least:

a) 8 < 9 < 10 1/2

b) 10 1/2 > 9 > 8

Step-by-step explanation:

We can use inequalities to order shoe sizes. We need to know what the symbols mean, for example < means "is lower than" while > means "is greater than". We know that 8 is lower than 9, and 9 is lower than 10 1/2 (which can be written also as 10.5), so we can write:

a) 8 < 9 < 10 1/2

The other way around would be to say that 10 1/2 is greater than 9, and 9 is greater than 8, which means:

b) 10 1/2 > 9 > 8

a

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.