University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2020
Views:

308

Pages:

3
Author:

Alma Hester

Unit 2-Logical Arguments and Line Relationships Writing Proofs (2.4) What is a postulate? a true statement that Cannot be proven Point, Line and Plane Postulates 2.1: Through any two distinct points there exists exactly one line 2.2: Through any three noncollinear points there exists exactly one plane 2.3: A line contains at least two points 2.4: A plane contains at least three points 2.5: If two distinct points lle in a plane, then the line through the pourts hes in the.. plarie distinct 2.6: If two lines intersect, then their intersection is exactly one point 2.7: If two distinct planes intersect, then their intersection is a line Match each diagram with one of the postulates stated above. 2.3 A. B. 2.7 2.1 C - D. 2.4 E 2.5 F 2.2 Translate the first four postulates into if-then form: Postulate 21: If there are two points, then there is exactly one line through them. Postulate 2.2: If there are three noncollinear points, then there is exactly one plane containing them. Postulate 2.3: If there is a line, then there are at least two points on the lime Postulate 2.4: If there is a plane, then there are at least three points on the plane. Sometimes, Always, or Never? 1. Two distinct points always lie in exactly one line. 2 Three distinct points Sometimes lie in exactly one line. 3. Three distinct points Sometimes ile in exactly one plane. 4 Three distinct collinear points never Ile in exactly one plane. 5 Two distinct planes Sometimes intersect. 6. Two distinct intersecting planes never intersect in exactly one point. 7 Two distinct Intersecting lines always Intersect in exactly one point. 8. Two distinct lines Sometimes intersect in exactly one point. 9. Two distinct intersecting lines always lie in exactly one plane. 10. A line and a point not on the line never lie in more than one plane. 11. A line never contains exactly one point. 12 When A and B are in a plane, line AB is always in that plane.