Given: a ∥ b and ∠1 ≅ ∠3 prove: e ∥ f we know that angle 1 is congruent to angle 3 and that line a is parallel to line b because they are given. we see that by the alternate exterior angles theorem. therefore, angle 2 is congruent to angle 3 by the transitive property. so, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem. which information is missing in the paragraph proof? ∠2 ≅ ∠4 ∠1 ≅ ∠2 ∠2 ≅ ∠3 ∠1 ≅ ∠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.

the answer is b.)

< 1=< 2

the correct answer is x/3+10≥32

hope this !

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: