One side of a triangle is 7 and another side is 10. Which of the values below could be the third side of the triangle?

x is the third side of the triangle, we have:

7 + 10 > x > 10 - 7

<=> 3 < x < 17

so the answer is C. III and IV only

C

Step-by-step explanation:

given 2 sides of a triangle, then the third side, x , is in the range

difference of 2 sides < x < sum of 2 sides , that is

10 - 7 < x < 10 + 7

3 < x < 17

The only values in the list between 3 and 17 are 4 and 16.

That is III and IV only → C

450 is the final answer! : )

∠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.