Chapter 2.4 Notes: Use Postulates and Diagrams

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Presentation transcript:

Chapter 2.4 Notes: Use Postulates and Diagrams Goal: You will use postulates involving points, lines, and planes.

Point, Line, and Plane Postulates: Through any two points there exists exactly one line. Postulate 6: A line contains at least two points. Postulate 7: If two lines intersect, then their intersection is exactly one point.

Postulate 8: Through any three noncollinear points there exists exactly one plane. Postulate 9: A plane contains at least three noncollinear points. Postulate 10: If two points lie in a plane, then the line containing them lies in the plane.

Postulate 11: If two planes intersect, then their intersection is a line. Ex.1: State the postulate illustrated by the diagram. a. b.

Ex. 2: Use the diagram to write examples of Postulates 9 and 10. Ex Ex.2: Use the diagram to write examples of Postulates 9 and 10. Ex.3: Use the diagram in Example 2. Which postulate allows you to say that the intersection of plane P and plane Q is a line?

Ex.4: Sketch a diagram showing intersecting at point W, so that . Ex.5: Sketch a diagram showing at its midpoint M. Perpendicular Figures: A line is a line perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point.

Ex.6: Which of the following statements cannot be assumed from the diagram? A, B, and F are collinear. E, B, and D are collinear. plane S plane T e. AF intersects BC at point B.