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Essentials of Geometry Day 1 Vocabulary and Segment Addition Name_________________________ Day 1 Warm Up 1. X + 13 = 22 4. -14 = - ( -2x + 2 ) 2. -6x -6x = 12 5. 6x – 2x + 8 = x + 5 3. -36 = 6 ( 2 – 8x ) 6. 3 ( 7x – 7 ) = -6 + 6x Points, Lines, and Planes Definition point – represented by a dot line – represented by a line with two arrowheads – written as AB plane – represented by a shape that looks like a floor or wall (need at least 3 points to name a plane) Sketch collinear points – points that lie on the same line coplanar points – points that lie in the same plane segment – written as AB ray – written as AB opposite rays – two rays that share an endpoint but go in opposite directions Example 1 Use the diagram to the right. H a. Name four points that are coplanar. J p L b. Name three points that are collinear. G K M Segments and Congruence The ______________________ between points A and B is the absolute value of the difference of the coordinates. Example 2 The distance from Ashville to Berkley is 3 miles. If John walks from Ashville to Berkley and Sarah walks from Berkley to Ashville, how far did each of them walk? Example 3 Find the distance between the two points given. a. b. 1 2 3 3 7 11 4 5 6 7 c. 15 19 23 27 5 10 15 20 25 30 35 AC Segment Addition A B C AB BC Example 4 Hilary drives from Charlotte to Duxbury which is 25 miles. Then she drives from Duxbury to Edmonton which is 17 miles. How far did she drive altogether? Example 5 Sam is going from Washington DC to Chicago. The two cities are 701 miles apart. If Sam has already driven 463 miles, how much farther does he have to go? Example 6 Find PQ. Example 7 Find GH. 36 29 O P 8 Find the indicated length. Example 8 Find VW. T F Q 3x 21 Example 9 Find YZ. 32 V x+8 W X G H 27 2x + 3 Y 3x - 1 Z