That means ∠4 and ∠6 are congruent to each other as well? But they're neither vertical nor corresponding. Here, all the odd numbered angles are congruent to each other and all the even numbered angles are congruent to each other. Since both vertical angles and corresponding angles are congruent, we can figure out all eight angles simply by knowing one of them! The term "supplementary" should be shining in neon lights inside your brain, possibly with the numbers 1, 8, and 0 doing a flashy burlesque number.ĭon't forget another critical part of any two intersecting lines: vertical angles. What should angles ∠ f and ∠ g add up to? Together, they make a straight angle, which means that if we add m∠ f + m∠ g, we should get a straight line. We can start by using what we already know. If there's anything math is good at, it's numbers. You want real numbers you can see, and we don't blame you. This congruence business is all good and fine, but it doesn't tell us anything about what these measurements actually are. You hardcore scientists out there are probably shifting in your seats. The three other pairs of corresponding angles are ∠ b and ∠ f, ∠ c and ∠ g, and ∠ d and ∠ h. Here, ∠ a and ∠ e are corresponding angles because they're in the same position relative to the transversal and their respective parallel line. Name all pairs of corresponding angles in this figure. Why, you ask? Since parallel lines have the same slope and a line always has a constant slope, it only makes sense that they intersect at the same angle measurement. You get the picture.īut what good are corresponding angles? We can't bake or juggle with them, so why is it even useful to know that two angles are corresponding? Well, that's because of the corresponding angle postulate, which says that corresponding angles formed by two parallel lines and a transversal line are congruent. Just the same, ∠3 corresponds to ∠7 and ∠4 to ∠8. In the figure above, ∠1 and ∠5 are corresponding. If two angles are in the same position compared to the transversal and one of the parallel lines, we call them corresponding angles. Ready for a truth bomb? When a transversal intersects two or more parallel lines, the two pairs of vertical angles formed at every intersection are the exact same. (Literally, since Jacob's a werewolf and all.) It makes things interesting, but a little hairy.
Think of it as the third wheel in a love triangle, like Jacob complicating matters between Edward and Bella. Get ready for some drama.Ī line that intersects a pair of parallel lines is called a transversal. So to keep things interesting, let's throw a monkey wrench into all of this and see just how strong their relationship is. All relationships have their problems, but parallel lines just keep chugging along perfectly. Well, parallel lines aren't like most couples. Just imagine if Marshall and Lily had never gotten together, if Ross and Rachel had been on a break, or if Harry had never met Sally. Two lines that go on forever without even meeting gets a bit dull, not to mention kind of depressing. Parallel lines are pretty special, but they tend to lose their luster really quickly.