8.1 Points, Lines, Planes, and Angles 455 Recall from Chapter 2 that the intersection > (symbolized ) of two sets is the set of elements (points in this case) common to both sets. Consider the rays hAB and hBA in Fig. 8.3(a). The intersection of hAB and hBA is the set of points that are common to both rays, or line segment AB, AB. Thus, h h AB BA AB. = > A B A B (a) (b) Solution: AB Solution: AB AB → → BA AB → → BA ↔ Intersection Union Figure 8.3 Did You Know? Let There Be Light A Kodak Camera advertisement appeared in the first issue of the Photographic Herald and Amateur Sportsman , in November 1889. The slogan “You press the button, we do the rest” summed up George Eastman’s groundbreaking snapshot camera system. Sunlight travels in straight lines, or rays. When these rays pass through a small hole of a darkened room, they converge and then spread out to form an inverted image of the sun on the opposite wall. In the eighteenth century, chemists discovered that certain salts of silver would darken when exposed to light, effectively creating a negative image. For the population at large, it all came together in 1888, when 23-year-old George Eastman, using basic geometric concepts, developed the first modern camera intended for the “casual millions,” which sold for $25 apiece. Today, digital cameras and smartphone cameras have almost replaced film cameras. Instead of focusing the image onto film, a digital camera focuses the image onto a semiconductor that records the image as a series of tiny colored dots called pixels. Also recall from Chapter 2 that the union < (symbolized ) of two sets is the set of elements (points in this case) that belong to either of the sets or both sets. The union of hAB and hBA is gAB (Fig. 8.3b). Thus, h h g AB BA AB = < Example 1 Unions and Intersections of Parts of a Line Refer to line AD below. Determine the following. A C D B → → AB DC Solution: AD A B C D h h AB DC AD = > b) h h AB DC < Once again ray AB and ray DC are shown below. The union of these two rays is that part of line AD that is part of either ray AB or ray DC. The union of ray AB and ray DC is the entire line AD, gAD → → AB DC Solution: AD ↔ A B C D h h g AB DC AD = < a) h h AB DC > b) h h AB DC < c) h AB CD > d) < AD CA Solution a) h h AB DC > Ray AB and ray DC are shown below. The intersection of these two rays is that part of line AD that is a part of both ray AB and ray DC. The intersection of ray AB and ray DC is line segment AD, AD. Rawpixel.com/Shutterstock
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