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