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If we find just one pair that works, then we know that the lines are parallel. Remind students that a line that cuts across another line is called a transversal. Various angle pairs result from this addition of a transversal. Next is alternate exterior angles. 2-2 Proving Lines Parallel Flashcards. How can you prove the lines are parallel? Proving Lines Parallel Worksheet - 3. Review Logic in Geometry and Proof. Thanks for the help.... (2 votes).

3.9 Proving Lines Parallel Answer Key

Essentially, you could call it maybe like a degenerate triangle. More specifically, they learn how to identify properties for parallel lines and transversals and become fluent in constructing proofs that involve two lines parallel or not, that are cut by a transversal. That angle pair is angles b and g. Both are congruent at 105 degrees. Students also viewed. They are also congruent and the same. And so we have proven our statement. Also, you will see that each pair has one angle at one intersection and another angle at another intersection. 2-2 Proving Lines Parallel | Math, High School Math, Geometry Models, geometry, parallel lines cut by a transversal, Perpendicular Lines. Alternate exterior angles are congruent and the same. Students are probably already familiar with the alternate interior angles theorem, according to which if the transversal cuts across two parallel lines, then the alternate interior angles are congruent, that is, they have exactly the same angle measure. This is line l. Let me draw m like this. 6x - 2x = 2x - 2x + 36 and get 4x = 36. if 4x = 36 I can then divide both sides by 4 and get x = 9. Proving Lines Parallel – Geometry.

First, you recall the definition of parallel lines, meaning they are a pair of lines that never intersect and are always the same distance apart. Their distance apart doesn't change nor will they cross. Explain that if ∠ 1 is congruent to ∠ 5, ∠ 2 is congruent to ∠ 6, ∠ 3 is congruent to ∠ 7 and ∠ 4 is congruent to ∠ 8, then the two lines are parallel. 3-5 proving lines parallel answer key. Both lines keep going straight and not veering to the left or the right. What I want to do in this video is prove it the other way around. Which means an equal relationship. Try to spot the interior angles on the same side of the transversal that are supplementary in the following example.

Then you think about the importance of the transversal, the line that cuts across two other lines. Draw two parallel lines and a transversal on the whiteboard to illustrate this: Explain that the alternate interior angles are represented by two angle pairs 3 and 6, as well as 4 and 5 with separate colors respectively. Note the transversal intersects both the blue and purple parallel lines. Alternate Exterior Angles. Since they are congruent and are alternate exterior angles, the alternate exterior angles theorem and its converse are called on to prove the blue and purple lines are parallel. When this is the case, only one theorem and its converse need to be mentioned. The picture below shows what makes two lines parallel. 3 5 proving lines parallel answer key. I say this because most of the things in these videos are obvious to me; the way they are (rigourously) built from the ground up isn't anymore (I'm 53, so that's fourty years in the past);)(11 votes). In review, two lines are parallel if they are always the same distance apart from each other and never cross. J k j ll k. Theorem 3.

3-5 Proving Lines Parallel Answer Key

This preview shows page 1 - 3 out of 3 pages. G 6 5 Given: 4 and 5 are supplementary Prove: g ║ h 4 h. Find the value of x that makes j ║ k. Example 3: Applying the Consecutive Interior Angles Converse Find the value of x that makes j ║ k. Proving Lines Parallel Worksheets | Download PDFs for Free. Solution: Lines j and k will be parallel if the marked angles are supplementary. If corresponding angles are equal, then the lines are parallel. Supplementary Angles.

For many students, learning how to prove lines are parallel can be challenging and some students might need special strategies to address difficulties. You can check out our article on this topic for more guidelines and activities, as well as this article on proving theorems in geometry which includes a step-by-step introduction on statements and reasons used in mathematical proofs. So I'll just draw it over here. The third is if the alternate exterior angles, the angles that are on opposite sides of the transversal and outside the parallel lines, are equal, then the lines are parallel. The last option we have is to look for supplementary angles or angles that add up to 180 degrees. There is one angle pair of interest here. Let me know if this helps:(8 votes). 3.9 proving lines parallel answer key. So if we assume that x is equal to y but that l is not parallel to m, we get this weird situation where we formed this triangle, and the angle at the intersection of those two lines that are definitely not parallel all of a sudden becomes 0 degrees. Using the converse of the corresponding angles theorem, because the corresponding angles a and e are congruent, it means the blue and purple lines are parallel. So, since there are two lines in a pair of parallel lines, there are two intersections. And so this leads us to a contradiction. Course Hero member to access this document. We also know that the transversal is the line that cuts across two lines.

These angle pairs are also supplementary. Still, another example is the shelves on a bookcase. What does he mean by contradiction in0:56? There is a similar theorem for alternate interior angles. Looking for specific angle pairs, there is one pair of interest. Based on how the angles are related. It might be helpful to think if the geometry sets up the relationship, the angles are congruent so their measures are equal, from the algebra; once we know the angles are equal, we apply rules of algebra to solve. Then it essentially proves that if x is equal to y, then l is parallel to m. Because we've shown that if x is equal to y, there's no way for l and m to be two different lines and for them not to be parallel. The video has helped slightly but I am still confused. Ways to Prove Lines Are Parallel. With letters, the angles are labeled like this.

Proving Lines Are Parallel

You may also want to look at our article which features a fun intro on proofs and reasoning. Using algebra rules i subtract 24 from both sides. And, both of these angles will be inside the pair of parallel lines. From a handpicked tutor in LIVE 1-to-1 classes. Remember, the supplementary relationship, where the sum of the given angles is 180 degrees.

I'm going to assume that it's not true. Converse of the Same-side Interior Angles Postulate. Angles on Parallel Lines by a Transversal. 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. Become a member and start learning a Member. Unlock Your Education. You would have the same on the other side of the road. So either way, this leads to a contradiction. To prove lines are parallel, one of the following converses of theorems can be used.

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. So given all of this reality, and we're assuming in either case that this is some distance, that this line is not of 0 length. 2) they do not intersect at all.. hence, its a contradiction.. (11 votes). Remember, you are only asked for which sides are parallel by the given information. If you subtract 180 from both sides you get. After 15 minutes, they review each other's work and provide guidance and feedback.