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Geo-Section 1.1

Undefined Terms in Geometry

Dioscorro
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Geo-Section 1.1

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  1. Do now • The distance around a polygon is called its ___________, and the distance around a circle is called its __________. • The number of square units covered by a figure is called its _____________.

  2. Section 1.1: identify points, lines, and planes SWBAT: use the defined notion of a point, line, and distance along a line to develop a definition for line segments. Geometry

  3. Undefined terms • Undefined Terms do not have a formal definition in geometry • Point: Has no dimension. Represented by a dot. • Line: Has one dimension. Represented by a line with two arrowheads, but it extends without end. • Through any two points there is one distinct line. You can use any two points on a line to name it. • Plane: Has two dimensions. Represented by a shape that looks like a floor, but it extends without end. • Through any three points not on the same line, there is exactly one plane. You can use any three points on a plane to name it (as long as they are not on the same line).

  4. Examples of undefined terms M Line , or Line AB, or Line BA Point A Point B Point C Plane M, or Plane ABC

  5. Types of points • Collinear Points: Lie on the same line • Coplanar Points: Lie in the same plane

  6. Example 1 • Give two other names for and for plane P. • Name three points that are collinear. • Name four points that are coplanar.

  7. Defined terms • Defined Terms can be described using known words such as point or line. • Segment(AKA Line Segment): Consist of two endpoints and all points on the line between those two points. • Ray: Consists of one endpoint and all the points in one direction on its line. • Opposite Rays: Rays beginning at the same endpoint, but going in opposite directions on the line.

  8. Examples of defined terms Use line as beginning term. Endpoints Ray AB or Opposite Rays: Segment AB, or , or

  9. Example 2 • Give another name for • Name all rays with endpoint D. Which of these rays are opposite rays?

  10. intersections • Two or more geometric figures intersect if they have one or more points in common. • The intersection of a figure is the set of points they have in common. q

  11. Example 3 • Sketch a plane and a line that is in the plane. • Sketch a plane and a line that does not intersect the plane. • Sketch a plane and a line that intersects the plane at a point.

  12. Example 4 • Sketch two different lines that intersect a plane at the same point.

  13. homework • Textbook pages 5-7 • #’s 3-6, 8, 9, 12, 15, 17, 18, 23, 26

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