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