Amaranth Degree Study Questions And Answers: 3.04Proving Lines Parallel.Docx - Name: Rj Nichol Date: 9/19 School: Rcva Facilitator: Dr. 3.04Proving Lines Parallel Are Lines X And Y Parallel? State | Course Hero

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3-2 Use Parallel Lines and Transversals. With letters, the angles are labeled like this. Proving lines parallel worksheets are a great resource for students to practice a large variety of parallel lines questions and problems. The parallel blue and purple lines in the picture remain the same distance apart and they will never cross. The converse of the interior angles on the same side of the transversal theorem states if two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are parallel. One more way to prove two lines are parallel is by using supplementary angles. The video has helped slightly but I am still confused. Examples of Proving Parallel Lines. I feel like it's a lifeline.

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There are several angle pairs of interest formed when a transversal cuts through two parallel lines. Alternate Exterior Angles. Geometry (all content). If we find just one pair that works, then we know that the lines are parallel. Benefits of Proving Lines Parallel Worksheets. He basically means: look at how he drew the picture. They are also corresponding angles. By the Congruent Supplements Theorem, it follows that 4 6.

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From a handpicked tutor in LIVE 1-to-1 classes. It is made up of angles b and f, both being congruent at 105 degrees. Show that either a pair of alternate interior angles, or a pair of corresponding angles, or a pair of alternate exterior angles is congruent, or show that a pair of consecutive interior angles is supplementary. Proving Parallel Lines. So, you have a total of four possibilities here: If you find that any of these pairs is supplementary, then your lines are definitely parallel. H E G 120 120 C A B.

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Remind students that the same-side interior angles postulate states that if the transversal cuts across two parallel lines, then the same-side interior angles are supplementary, that is, their sum equals 180 degrees. Or another contradiction that you could come up with would be that these two lines would have to be the same line because there's no kind of opening between them. The angles created by a transversal are labeled from the top left moving to the right all the way down to the bottom right angle. You would have the same on the other side of the road. Example 5: Identifying parallel lines (cont. So, say that my top outside left angle is 110 degrees, and my bottom outside left angle is 70 degrees. Both lines keep going straight and not veering to the left or the right. After 15 minutes, they review each other's work and provide guidance and feedback. Solution Because corresponding angles are congruent, the boats' paths are parallel.

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Terms in this set (6). What I want to do in this video is prove it the other way around. This preview shows page 1 - 3 out of 3 pages. X + 4x = 180 5x = 180 X = 36 4x = 144 So, if x = 36, then j ║ k 4x x. H E G 58 61 B D Is EB parallel to HD? Become a member and start learning a Member. At this point, you link the railroad tracks to the parallel lines and the road with the transversal.

Proving Lines Parallel Quiz

Now, point out that according to the converse of the alternate exterior angles theorem, if two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel. What does he mean by contradiction in0:56? Another example of parallel lines is the lines on ruled paper. Still, another example is the shelves on a bookcase. So I'll just draw it over here. Converse of the Same-side Interior Angles Postulate. Alternate interior angles is the next option we have.

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And, both of these angles will be inside the pair of parallel lines. Angle pairs a and d, b and c, e and h, and f and g are called vertical angles and are congruent and equal. Divide students into pairs. Teaching Strategies on How to Prove Lines Are Parallel. One might say, "hey, that's logical", but why is more logical than what is demonstrated here? You much write an equation. Let's say I don't believe that if l || m then x=y. And so this line right over here is not going to be of 0 length. In your lesson on how to prove lines are parallel, students will need to be mathematically fluent in building an argument. Not just any supplementary angles. And so we have proven our statement. Important Before you view the answer key decide whether or not you plan to.

Sometimes, more than one theorem will work to prove the lines are parallel. The corresponding angle theorem and its converse are then called on to prove the blue and purple lines parallel. What we are looking for here is whether or not these two angles are congruent or equal to each other. Activities for Proving Lines Are Parallel. And then we know that this angle, this angle and this last angle-- let's call it angle z-- we know that the sum of those interior angles of a triangle are going to be equal to 180 degrees. This is the contradiction; in the drawing, angle ACB is NOT zero. So let's put this aside right here.

Students also viewed. I am still confused. How can you prove the lines are parallel? Explain that if the sum of ∠ 3 equals 180 degrees and the sum of ∠ 4 and ∠ 6 equals 180 degrees, then the two lines are parallel. Prepare additional questions on the ways of proof demonstrated and end with a guided discussion. And so this leads us to a contradiction.

So this angle over here is going to have measure 180 minus x. You can cancel out the +x and -x leaving you with. Or this line segment between points A and B. I guess we could say that AB, the length of that line segment is greater than 0. That angle pair is angles b and g. Both are congruent at 105 degrees. So when we assume that these two things are not parallel, we form ourselves a nice little triangle here, where AB is one of the sides, and the other two sides are-- I guess we could label this point of intersection C. The other two sides are line segment BC and line segment AC.

So let's just see what happens when we just apply what we already know. They should already know how to justify their statements by relying on logic. One could argue that both pairs are parallel, because it could be used, but the problem is ONLY asking for what can be proved with the given information.