A triangle has rotation symmetry that can take any of its vertices to any of its other vertices. Select ALL conclusions that we can reach this. A. All sides of the triangle have the same length

B. All angles of the triangle has the same measure

C. All rotations take one half of the triangle to the other half of the triangle

D, it is a right triangle

E. None of the sides of the triangle have the same length

F. None of the angles of the triangle have the same measure

c e f

Step-by-step explanation:

C. All rotations take one half of the triangle to the other half of the triangle

E. None of the sides of the triangle have the same length

F. None of the angles of the triangle have the same measure

∠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.

b

step-by-step explanation: