Geometry – Properties of Parallel Lines
This lesson investigates and use the alternate interior angles theorem, the alternate exterior angles theorem, the corresponding angles postulate, the same side interior angles theorem and the same side exterior angles theorems.
The use of a two column proof to show that 2 angles are supplementary, but the angles are not able to be proved with a theorem or postulate. The proof takes three or four steps.
Another problem in the video lesson below is finding the measure of angles when give two parallel lines and a transversal. There are two types of these problems. The first type of finding the measure of an angle is when you are given the actual measure of the angle such as 50 degrees. You are able to find the measure of every angle formed by 2 parallel lines and a transversal, when you know the measure of one. If one angle measures 50 degrees, all of the every angle in the diagram will be 50 or 130 degrees. All angles are either congruent or supplementary in this situation.
The other type of find the measure of an angle problem is when you are given two or more algebraic expressions instead of real numbers as the measurements. For example you are given the
measure of angle 1 = 3x + 7 (1)
measure of angle 6 = 5x + 15 (2).
You need to find the value of x that makes the lines parallel. It will be
3x + 7 = 5x + 15, (3)
Equation 3 is the result of the angles having a congruent relationship as with alternate interior angles, alternate exterior angles and corresponding angles. If the angles are same side interior angles or same side exterior angles, then the equation would be:
(3x + 7) + (5x + 15) = 180 (4)
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.
Here is the second video.
Filed under: Geometry, Properties of Parallel Lines Tagged: | alternate exterior angles, alternate exterior angles theorem, alternate interior angles, alternate interior angles theorem, corresponding angles, corresponding angles postulate, Geometry, same side exterior angles theorem, same side exterior angles, same side interior angles, same side interior angles theorem, transversal