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Section 1.1 Points, Lines, and Planes ­ All geometric shapes are made of points. ­ In Geometry you will learn about those shapes and their characteristics. ­ A point is simply a location. ­ A line is made up of points and has no thickness or width. A B n ­ Points on the same line are said to be collinear. ­ A plane is a flat surface made up of points. X Y Z T ­ Points that lie on the same plane are said to be coplanar. 1 ­ A plane has no depth and extends infinitely in all directions. ­ Points are often used to name lines and planes. ­ The letters of the points can be in any order. 2 Ex 1 Use the figure to name each of the following: a. a line containing point A b. a plane containing point C Ex 2 Name the geometric shapes modeled by the picture. 3 Ex 3 Name the geometric shape modeled by each object. a. the long hand on a clock b. a 10 x 12 patio c. the location where the corner of a driveway meets the road ­ In geometry, point, line, and plane are considered undefined terms because they are only explained using examples and descriptions. 4 Ex 4 Draw and label a figure for each relationship. a. Lines GH and JK intersect at L for , , and K(2,­3) on a coordinate plane. Point M is coplanar with these points, but not collinear with GH and JK. b. TU lies in plane Q and contains point R. c. plane R contains lines AB and DE, which intersect at point P. Add point C on plane R so that it is not collinear with AB or DE. d. QR on a coordinate plane contains P(4,­4) and Q (­2,4). Add point T so that T is collinear with these points. 5 ­ Space is a boundless, three­dimensional set of all points. ­ Space contains lines and planes. Ex 5 a. How many planes appear in this figure? b. Name three points that are collinear. c. Are points G, A, B, and E coplanar? Explain. d. At what point do EF and AB intersect? 6 Modeling Intersecting Planes Activity 1. Draw a line where the two planes meet. The intersection of two planes is a line, so let’s label two points on the line, C and D. 2. Draw a point F on your model so that it lies in Q but not in R. Can F lie on DC? 3. Draw point G so that it lies in R, but not in Q. Can G lie on DC? 4. If point H lies in both Q and R, where would it lie? Draw point H on your model. 5. Draw a sketch of your model on paper. Label all points, lines, and planes appropriately. Assign Pgs. 9 ­ 11 # 4 ­ 10, 12 ­ 18, 21 ­ 27, 30 ­ 35, 37, 41, 43 Pg. 12 Read page and do # 1, 2 7 Example 1 Draw 3 planes that do not intersect. Example 2 Draw plane W. Line BC lies in plane W, line AD intersects plane W at point E. Example 3 Lines a, b, and c are coplanar, but do not intersect. 8