Parallel and Perpendicular Lines – Geometry – 3.3

This lesson is about the parallel lines theorem, the perpendicular to same line theorem and the perpendicular to one line theorem. Now, these are shorter names that I have given these theorems.

The Parallel Lines Theorem

If two lines are parallel to the same line,
then they are parallel to each other.

The Perpendicular to Same Line Theorem

In a plane, if two lines are perpendicular to the same line,
then they are parallel to each other.

The Perpendicular to One Line Theorem

In a plane, if a line is perpendicular to one of two parallel
lines, the it is also perpendicular to the other.

The first problem covered in the video is working with frame making. It is not the best I have ever done, but I will be putting something together in the near future to add to this
post.

The second problem is a paragraph proof involves proving two lines parallel. The diagram involves three lines that appear to be parallel that are in the order from top to
bottom, lines a, b and c. There are two transversals, but only one is labeled line s. Line is is perpendicular to lines a and c and lines a and b are parallel. We must prove c is parallel to b. From given, it can be established that b is perpendicular to s because of the Perpendicular to One Line Thm. Now we can state that c is parallel to b because of the
Perpendicular to Same Line Thm. QED

If you have a specific question, please ask. Cite your book, I might have it and I can show the specific problem. Also, give your best description of the problem that you can. You must quote the question from your book, which means you have to give the name and author with copyright date. I have used digital images of problems I have worked out by hand for the Algebra 2 portion of my blog.

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