Applied Geometry

Applied Geometry Lesson 1-3 Postulates Objective: Learn to identify and use basic postulates about points, lines, and planes.

Postulate • Postulate – statements in geometry that are accepted as true.

Postulate 1-1 • Two points determine a unique line How many lines could I draw through the 2 points?

Postulate 1-2 • If two distinct lines intersect, then their intersection is a point.

Postulate 1-3 • Three noncollinear points determine a unique plane There is only one plane that contains points A, B, and C

Example Points D, E, and F are noncollinear • Name all of the different lines that can be drawn through these points. • Name the intersection of point E

Your turn • Points Q, R, S, and T are noncollinear. Name all of the different lines that can be drawn through these points. Name the intersection of

Example • Name all of the planes that are represented in the figure. plane ACG, plane AGH, plane ACH, plane CGH

Example • Name all of the planes that are represented in the figure Plane ACF, plane BEF, plane ABE, plane ABC, plane DEF

Postulate 1-4 • If two distinct planes intersect, then their intersection is a line.

Example • The figure shows the intersection of six planes. Name the intersection of plane CDG and plane BCD. • Name two planes that intersect in Plane BCD and plane ABH *hint: use any of the 4 points to name the plane, must name around the plane

Example • Name the intersection of plane ABC and plane DEF.

Applied Geometry