![]() ![]() The degree measures run in both directions to end at 180°. The outer scale starts at zero (0) on the right near B and the inner scale starts on the left, near point A. The 2 scales on a protractor, allow us to measure clockwise or counter-clockwise angles. Since we're learning to measure angles in this lesson, we'll study how to use the protractor. The table of equivalences is:ġ° (degree) = 60' (minutes) and 1' (minute) = 60" (seconds).Īs always in math, there are symbols ( °, ', and " ) to represent degrees, minutes and seconds. When we measure angles, the largest units are called degrees instead of hours. On the clock, an hour (largest unit) is divided into 60 minutes, and each minute is divided into 60 seconds. We still use it today on our clocks to tell time and to measure angles. These tools allow us not only to measure but also to construct angles.Īncient mathematicians and scientists used a sexagesimal system based on the number 60 to measure angles because they most often measured the circular motion of the sun, moon and stars. When we open our first geometry kit, we see it includes a ruler, 2 right triangles, a set of compasses and a protractor (diagram). In triangle XYZ, we know exactly which angle we mean when we say angle X, so in such a case, 1 letter will do. But in the next picture, there are four different angles at B, namely angles ABD, ABE, DBC and CBE, so if I say angle B, which one do I mean? Therefore, it's best to use 3 letters to name an angle if there are many angles at a common vertex. In the diagram above, it's easy to see what angle we mean when we say angle B. Sometimes, we use only 1 letter to name an angle, but that can be confusing when there's more than one angle at the same vertex. The angle above can be named either ABC or CBA - note that B, the vertex, is in the middle, between A and C. We generally name angles like the one in the diagram above with 3 letters and we always put the vertex letter between the other two just the way it appears in the picture. They rotate around a fixed point - (if they didn't, they'd fly off the bus) - through an angle large enough so that together, they wipe enough of the windshield for the driver to see clearly. Think about the windshield wipers on the school bus. Turning is also called rotating - so angles are the result of a rotation or turn. Once we've got the cover of our math book open, we TURN the page. Then we turned BA upwards to create the angle ABC. It's as if BA started out lying on top of BC, pinned down at B. ![]() The line segments AB and BC are the arms.īC is called the initial arm and AB is called the terminal arm. The point where they meet on the book's spine, is the vertex. With our book, the bottom edges of the cover and first page are the arms and The lines that form the angle are called arms. The point at which the lines meet is called the vertex. When you open your math book part way as in the picture, the bottom edge of the cover forms an acute angle with the bottom edge of the first page.Īn angle is formed when 2 lines meet at a point. In more advanced math courses, we'll call this ray a vector. Note: QP is a ray which has direction so we must name it in the correct order. The small black square is used to indicate 90°. Perpendicular lines meet at right angles forming four 90° angles at their intersection. ![]() Intersecting lines cross each other at a single point. We name or label it by the endpoint and any other point on it. X is the midpoint so SX = XT.Ī ray is a part of a line that extends indefinitely in one direction from one endpoint. We name or label a line by indicating any two points on it.Ī line segment is a part of a line precisely defined and named by two endpoints. When we join A to B, B to C and C to A, we haveģ line segments that define a triangle ABC.ĬDor DC is a line - a path of points extending forever in opposite directions. We use a dot - not a potato! - to represent it, then we name or label it with an upper case (Capital) letter. Once we've heard the expression "a ray of sunshine" we know instinctively what it means.Įach ray of sunshine starts at the sun - a point in space,Īnd continues on forever, in one direction.Ī point is a precise location or spot in space. One term we'll discuss that we generally use correctly is a ray. Geometry, however, demands that we use precise terms to define things, so let's learn to call lines, points and angles by their mathematically correct names. In everyday speech, most of us use the word "line" incorrectly. Points turn into lines, then lines become the sides or arms of angles when they intersect each other. The 3-dimensional space in which we live is made up of points, lines and angles. ![]()
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