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