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![parallel lines and transversals parallel lines and transversals](https://showme0-9071.kxcdn.com/files/28511/pictures/thumbs/2163283/last_thumb1445952784.jpg)
Again, you need only check one pair of alternate interior angles! Supplementary Angles
![parallel lines and transversals parallel lines and transversals](https://image1.slideserve.com/3458082/transversal-l.jpg)
Or, if ∠ F is equal to ∠ G, the lines are parallel. So, in our drawing, if ∠ D is congruent to ∠ J, lines M A and Z E are parallel. If two lines are cut by a transversal and the alternate interior angles are equal (or congruent), then the two lines are parallel. If just one of our two pairs of alternate exterior angles are equal, then the two lines are parallel, because of the Alternate Exterior Angle Converse Theorem, which says: Here are both pairs of alternate interior angles: Here are both pairs of alternate exterior angles: Can you find another pair of alternate exterior angles and another pair of alternate interior angles? ∠ D is an alternate interior angle with ∠ J. In our drawing, ∠ B is an alternate exterior angle with ∠ L. They cannot by definition be on the same side of the transversal. Can you identify the four interior angles?Īlternate angles appear on either side of the transversal. In our drawing, ∠ B, ∠ C, ∠ K and ∠ L are exterior angles. Interior angles lie within that open space between the two questioned lines. Exterior angles lie outside the open space between the two lines suspected to be parallel. Alternate AnglesĪlternate angles as a group subdivide into alternate interior angles and alternate exterior angles. If you check only a single pair of corresponding angles and they are equal, then the two lines are parallel. We want the converse of that, or the same idea the other way around: The Corresponding Angles Postulate states that parallel lines cut by a transversal yield congruent corresponding angles. These eight angles in parallel lines are:Įvery one of these has a postulate or theorem that can be used to prove the two lines M A and Z E are parallel. Let's label the angles, using letters we have not used already: Angles In Parallel Lines Those eight angles can be sorted out into pairs. Create a transversal using any existing pair of parallel lines, by using a straightedge to draw a transversal across the two lines, like this: When cutting across parallel lines, the transversal creates eight angles. Other parallel lines are all around you:Ī line cutting across another line is a transversal. If the two rails met, the train could not move forward. If you have ever stood on unused railroad tracks and wondered why they seem to meet at a point far away, you have experienced parallel lines (and perspective!). For example, to say line J I is parallel to line N X, we write: To use geometric shorthand, we write the symbol for parallel lines as two tiny parallel lines, like this: ∥. Both lines must be coplanar (in the same plane). Two lines are parallel if they never meet and are always the same distance apart. By using a transversal, we create eight angles which will help us. How can you prove two lines are actually parallel? As with all things in geometry, wiser, older geometricians have trod this ground before you and have shown the way.
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