ā 1ā
ā 2 by the alternate exterior angles theorem.
step-by-step explanation:
given, a ā„ b and ā 1 ā
ā 3 .we have to prove that e ā„ f
we know that ā 1ā
ā 3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ā 2ā
ā 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 ā 1ā
ā 3 and by transitivity property ā 2ā
ā 3 .
hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ā 1.
the only options in which ā 1 is present are ā 1 and ā 2, ā 1 and ā 4
ā 1 and ā 4 is not possible āµ after applying transitivity we didn't get ā 4.
hence, the missing statement is ā 1ā
ā 2.
so, ā 1ā
ā 2 by the alternate exterior angles theorem.