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1.1 Identify Points, Lines and Planes

1.1 Identify Points, Lines and Planes

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1.1 Identify Points, Lines and Planes

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  1. 1.1 Identify Points, Lines and Planes Undefined Terms (terms that do not have formal definitions but have an understood meaning) Point Line Plane

  2. 1.1 Identify Points, Lines and Planes Point: has no dimension. It is represented by a dot.  Line: has one dimension. It is represented by a line with two arrowheads, but it extends without end. Plane: has two dimensions. It is represented by a shape that looks like a floor or a wall, but it extends w/o end.

  3. 1.1 Identify Points, Lines and Planes Collinear points are: Points that lie on the same line. Coplanar points are: Points that lie on the same plane.

  4. 1.1 Identify Points, Lines and Planes Example 1: • Give two other names for Line PQ and for plane R. b. Name three points that are collinear and Name four points that are coplanar.

  5. 1.1 Identify Points, Lines and Planes Defined terms: terms that can be described using known words. Segment: the line segment AB, or segment AB, consists of the endpoints A and B and all the points that lie on line AB that are between A and B. Ray: The ray AB consists of the endpoint A and all the points on line AB that lie on the same side of A as B.

  6. 1.1 Identify Points, Lines and Planes If C lies on line AB between A and B, then ray CA and ray CB are opposite rays. Segments and rays are collinear if they lie on the same line. So, opposite rays are collinear. Lines, segments and rays are coplanar if they lie on the same plane.

  7. 1.1 Identify Points, Lines and Planes EXAMPLE 2: • Give another name for Segment PM. • Name all rays with endpoint Q. Which of these rays are opposite rays?

  8. 1.1 Identify Points, Lines and Planes Two or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common. The intersection of The intersection of two lines is a point. two planes is a line.

  9. 1.1 Identify Points, Lines and Planes Example 3: • Sketch a plane and two intersecting lines that intersect the plane at separate points. • Sketch a plane and two intersecting lines that do not intersect the plane. • Sketch a plane and two intersecting lines that lie in the plane.

  10. 1.1 Identify Points, Lines and Planes Example 3: d. Sketch a plane and a line that is in the plane. e. Sketch two planes that do not intersect in a line. f. Sketch three lines that lie in a plane and intersect at one point.

  11. 1.1 Identify Points, Lines and Planes • Can two planes intersect in a segment? Explain. • Can a line intersect a plane in only two points? Explain.