Help Would Be Much Appreciated Constructing Parallel and Perpendicular Lines Construct the following using a pencil, straightedge and a compass. Include step by step explanations for each construction.
1. Given a point on a line, construct the perpendicular to the line at the given point.
2. Given a point not on a line, construct the perpendicular to the line from the given point.
3. Given a point not on a line, construct the parallel to the given line through that point not on the line.
4. Construct 3 lines parallel to each other.

think about it deeply and passionately about this property

i am sorry

∠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.

answer: no, but if it does it's a obvious pattern.

step-by-step explanation: