Item 15 The coordinates of the midpoint of $\overline{GH}$ are $M\left(8,\ 0\right)$ and the coordinates of one endpoint are $H\left(-2,\ 9\right)$ .

The coordinates of the other endpoint are

Step-by-step explanation:

G(18,-9)

The coordinates of the midpoint of GH are M (8,0) and the coordinates of one endpoint are H(-2, 9). We need to find the coordinates of G. Let G is (x,y).It can be done using mid point formula i.e.

So,

∠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.