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Points, Lines, and Planes

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Presentation on theme: "Points, Lines, and Planes"— Presentation transcript:

1 Points, Lines, and Planes
Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Points, Lines, and Planes In this lesson, you will learn basic geometric facts to help you justify your answer to the Solve It. Geometry Foundations, pg 10

2 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Focus Question How do you name points, lines, planes, segments, and rays? In geometry, some words such as point, line, and plane are undefined. Undefined terms are the basic ideas that you can use to build the definitions of all other figures in geometry. Although you cannot define undefined terms, it is important to have a general description of their meanings. Geometry Foundations, pg 4

3 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Geometry Foundations, pg 10

4 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 1 Points that lie on the same line are collinear points. Points and lines that lie in the same plane are coplanar. All the points of a line are coplanar. Geometry Foundations, pg 11

5 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 1 The terms point, line, and plane are not defined because their definitions would require terms that also need defining. You can, however, use undefined terms to define other terms. A geometric figure is a set of points. Space is the set of all points in three dimensions. Similarly, the definitions for segment and ray are based on points and lines. Geometry Foundations, pg 11

6 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 1 Geometry Foundations, pg 11

7 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 1 Geometry Foundations, pg 12

8 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 1 Geometry Foundations, pg 12

9 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 14

10 Ch 1-2 Part 2 Focus Question
Students will be able to understand basic terms and postulates of geometry. Part 2 Focus Question How do you find the intersection of two planes? A postulate or axiom is an accepted statement of fact. Postulates, like undefined terms, are basic building blocks of the logical system in geometry. You will use logical reasoning to prove general concepts in this book. Geometry Foundations, pg 14

11 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 You have used some of the following geometry postulates in algebra. For example, you used Postulate 1-1 when you graphed equations such as y = 2x You graphed two points and drew the line through the points. Geometry Foundations, pg 14

12 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 When you have two or more geometric figures, their intersection is the set of points the figures have in common. Geometry Foundations, pg 14

13 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 There is a similar postulate about the intersection of planes. Geometry Foundations, pg 15

14 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 When you know two points that two planes have in common, Postulates 1-1 and 1-3 tell you that the line through those points is the intersection of the planes. Geometry Foundations, pg 15

15 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 15

16 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 When you name a plane from a figure like the box in Problem 3, list the corner points in consecutive order. For example, plane ADCB and plane ABCD are also names for the plane on the tope of the box. Plane ACBD is not. Geometry Foundations, pg 16

17 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Photographers use three-legged tripods to make sure that a camera is steady. The feet of the tripod all touch the floor at the same time. You can think of the feet as points and the floor as a plane. As long as the feet do not all lie in one line, they will lie in exactly one plane. This illustrates Postulate 1-4. Geometry Foundations, pg 16

18 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 16

19 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 16

20 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 16

21 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 17

22 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 17

23 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 18

24 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 18

25 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 18

26 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 18

27 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 18

28 Ch 1-2 Students will be able to understand basic terms and postulates of geometry. Part 2 Geometry Foundations, pg 18

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