Lines, Segments, Rays, and Angles


 Willis Cameron
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1 Line and Angle Review Thursday, July 11, :22 PM Lines, Segments, Rays, and Angles Slide Notes Title Lines, Segment, Ray A line goes on forever, so we use an arrow on each side to indicate that. You name the line by using two letters on the line. The are labeled with a letter of the alphabet so that we can easily talk about the line  it has a name. Other lines might use different letters. It is all up to the one that draws it. A segment is much like a line. It is straight, but instead of Saxon 2_ 3rd ed Page 1
2 Lines, Segment, Ray A line goes on forever, so we use an arrow on each side to indicate that. You name the line by using two letters on the line. The are labeled with a letter of the alphabet so that we can easily talk about the line  it has a name. Other lines might use different letters. It is all up to the one that draws it. A segment is much like a line. It is straight, but instead of going on forever, it ends at points on the line. Like the line, a segment can be labeled. This time the little symbol above the letters show a line or can be a line with endpoints. A ray is a little of both a line and a segment. It ends on one side but goes on and on forever to the other direction. The ray symbol is used above its two letter name to show it is a ray. Math with Segments If we write the name of a line in letters without the bar above them, we are talking about the length of the line. You can see that here in this problem. If AC is 13 units and line segment AB is 3 units, how long is the line segment BC? Here is how you solve it A to C is the total length of the line between the furthest points that all three points share. The segment AB and BC will add up to it. The total of 13 units minus the part of 3 units equals 10 units. Parallel Lines Two straight lines in the same plane, such as a piece of paper or a chalkboard, could intersect or be parallel if you extend them out forever. When they never cross, you have parallel lines. These lines stay at the same distance apart at all times. Saxon 2_ 3rd ed Page 2
3 Intersecting Lines When straight lines cross, you have intersecting lines. An interesting thing about these is that the angles that are opposite each other will have the same measure. So the angles you see here in orange are equal and the angles you see in white are equal to each other. Perpendicular Lines A special type of intersecting line is a perpendicular line. When these cross, they form ninety degree angles or square corners. Saxon 2_ 3rd ed Page 3
4 Right Angles Those ninety degree angles or square corners pop up in squares, rectangles, triangles and just angles by themselves. Note that 90 degree angles will often be indicated by a square. Acute and Obtuse Angles Angles that are less than 90 degrees can be classified as acute angles. When they open up greater than 90 degrees but they are less than a straight line, they are obtuse. Straight and Reflex Angles Straight angles make a straight line. Another way to think of a straight line is an angle that is opened up 180 degrees. When an angle is greater than a straight angle but less than 360 degrees, it is a reflex angle. Saxon 2_ 3rd ed Page 4
5 Angle Notation As with the line, segment, and ray, we need a way to name angles. When there is just one of them, a simple angle symbol and a letter is fine to name it. When there is more than one angle, you start labeling the ends with letters and use all three to name each angle combination. Here is angle TAZ While here is angle KAZ When angles share a common vertex, they are called adjacent angles. Complementary vs. Supplementary Angles When a 90 degree angle is split, we say that the two adjacent angles are complementary to each other. When a straight angle is split, the two are supplementary angles. The nice thing about these two is that since you know what they should both add up to, either 180 or 90 degrees, if you know one of the angles, you can compute the other one. Saxon 2_ 3rd ed Page 5
6 Protractor This is a protractor. It is a useful tool for measuring and creating angles. Measure and Angle Let's use the protractor to determine the angle. Line up the line that marks the center of the ruler at the bottom with the vertex of the angle. You want the protractor to follow along one of the sides of the angle. There are two sets of measurements. The inner one zeros on the right and the outer one zeros on the left. Assuming that you want the inner angle select the one that would fall inside the angle. Now look where the angle's line crosses the protractor to get the measurement. This one is 120 degrees. Create an Angled Ray 1 Sometimes you need to create the angle from scratch. You don't always even need to draw a two lined angle because even a ray can have an angle measure. It is almost as if the invisible horizon line is its other half. Let's draw a ray that is 40 degrees compared to the horizon line. Get as close as you can to making the protractor parallel to the top and bottom edge of the surface you are drawing on. Mark the point near the midline and one at the 40 degree point on the protractor starting from the zero on the right side. Saxon 2_ 3rd ed Page 6
7 Create an Angled Ray 2 Now use the straight edge of the protractor to connect the two marks to make the ray. Create an Angled Ray 3 Now you have a 40 degree ray. Saxon 2_ 3rd ed Page 7
8 Important Angles There are certain angles that are more important than others in mathematics. O degrees is the point from where you start, but in an angle that is 360 degrees it wraps all the way back to where it started. 180 degrees makes a straight angle. Half of that makes 90 degrees. Across from ninety and the midway point between 180 and 360 is the 270 degree angle. Split the ninety degree angle and you have a 45 degree angle. All of these angles pop up over and over again in mathematics as well as out in the real world. 180 and 360 Degrees Circles are basically 360 angles. A semicircle, or half circle, would be half that, 180 degrees. Show What You Know Time now to show what you know. I am going to call out some angle or line types and you click on the image that is the best example of it. Straight angle Perpendicular lines Intersecting, but not perpendicular lines An acute angle A reflex angle Obtuse angle Right angle Saxon 2_ 3rd ed Page 8
9 Parallel lines Supplementary angles Complementary angles. Show What Your Know Now let's have you take what you know and use it to find some unknown angles. What angle in white is shown? Compute it from the angles you are given and what you have learned about complement and supplement angles. Show What You Know Now try this one. Think about what you have learned about intersecting lines. Saxon 2_ 3rd ed Page 9
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