Geometry Basics: Points, Lines, and Planes

Learn about the fundamental concepts in geometry such as points, lines, and planes, along with their characteristics and relationships. Explore undefined and defined terms, collinear and coplanar points, line segments, rays, and opposite rays.

• Geometry Basics
• Point Line Plane
• Undefined Terms
• Defined Terms
• Collinear Points

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1. DO NOW 1 1. The distance around a polygon is called its ___________, and the distance around a circle is called its __________. 2. The number of square units covered by a figure is called its _____________.

2. SECTION 1.1: IDENTIFY POINTS, LINES, AND PLANES 2 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 3 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 4 ? M Line ?, or Line AB, or Line BA Point A Point B Point C Plane M, or Plane ABC

5. TYPES OF POINTS 5 Collinear Points: Lie on the same line Coplanar Points: Lie in the same plane

6. EXAMPLE 1 6 1. Give two other names for ?? and for plane P. 2. Name three points that are collinear. 3. Name four points that are coplanar.

7. DEFINED TERMS 7 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 8 Use line ?? as beginning term. Endpoints Ray AB or ?? Opposite Rays: ?? ?? Segment AB, or ??, or ??

9. EXAMPLE 2 9 1. Give another name for ??. 2. Name all rays with endpoint D. Which of these rays are opposite rays?

10. INTERSECTIONS 10 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 11 1. Sketch a plane and a line that is in the plane. 2. Sketch a plane and a line that does not intersect the plane. 3. Sketch a plane and a line that intersects the plane at a point.

12. EXAMPLE 4 12 1. Sketch two different lines that intersect a plane at the same point.

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