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![]() You mark drawings of parallel lines with little bird-feet marks, like Vs on their sides. Yes, we have a H A R E crossing a L I O N. The two points where H E crosses the parallel lines are P o i n t s A and R. Let's create parallel lines L I and O N, and a transversal H E. We are interested in the four interior lines, those are our Alternate Interior Angles. Four of those angles are exterior and four are interior. When the transversal intersects, it creates four angles at each parallel line, or eight angles altogether. Just beyond the line and between it and the parallel line next to it, is the interior. You would be outside, at the exterior, of the parallel lines. Think about it: if you were two-dimensional and came across a line in your path, that line would stretch infinitely in two directions and you could not get past it. When a transversal intersects parallel lines, it creates an interior and exterior. A transversal intersecting parallel lines at 90 ° is perpendicular. Any line cutting across parallel lines is a transversal. Parallel lines can be intersected by transversals. While two points determine a line, if you locate three points on a line, you have created a straight angle with the middle point as the vertex. The only sneaky way to get an angle from parallel lines is to declare each line is a straight angle, with a measure of 180 °. The two lines, line segments, or rays never converge (move closer) or diverge (move away). Unlike the intersecting rays Z A and Z U, parallel lines never meet. They could be snippets cut as rays or as line segments, depending on taking an infinite chunk or a finite chunk of the infinite, intersecting lines. We say rays Z A and Z U, but those rays could also be small snippets out of longer lines that intersected at P o i n t Z. Where they meet at P o i n t Z, they form a vertex, ∠ Z.Two rays, Z A and Z U, meet at P o i n t Z.Something as simple as an angle has parts. ![]() We almost never write " a n g l e Z," using instead a quick shorthand, ∠ Z. Parts of an Angleįor example, let's construct a n g l e Z. You trade a lot of number-crunching (not much addition, multiplication, subtraction or division in geometry) for a lot of inventory. Sometimes geometry feels like a giant parts warehouse. Alternate Interior Angles (Definition, Theorem, & Examples)
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