1. a sphere is sliced so that the cross section does not intersect the center of the sphere.
what is the shape of the cross section?
square
circle
rectangle
semicircle
2. what is the area of a cross section that is parallel to face abcd ?
3. what is the area of the two-dimensional cross section that is parallel to face abc ?
4. this rectangular prism is intersected by a plane that contains points b, d, h, and f.
what is the perimeter of the cross section?
(the first picture is for 2, the second is for 3, the third is for 4)

∠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.