6. (10 pts) recall the cosine formula: if a triangle has side lengths a, b and c, and the angle between the sides of length a and b is e, then c^2 = a^2 +b^2+2ab cose. (a) restate the cosine formula as a statement about vectors v and w with angle 8 between them. (b) use what you know about dot products to prove the above formulation of the cosine formula

the reason why your question keeps getting deleted because this is not a school related question : )

i will answer your question though.

i never tried church's

∠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.