Here is a geometric figure containing points, lines, and planes:
o
|
|
o ----- o
/ \
/ \
o o
In this figure, there are three points labeled "o" and two lines connecting them. There are also two planes, one containing the three points on the left and one containing the three points on the right.
To create this figure, we used the following postulates:
Postulate 1 (Ruler Postulate): The points on a line can be put into a one-to-one correspondence with the real numbers.
Postulate 2 (Segment Addition Postulate): If B is between A and C, then AB + BC = AC.
Postulate 3 (Plane Postulate): Through any three noncollinear points, there is exactly one plane.
Postulate 4 (Line Postulate): If two points lie in a plane, then the entire line containing those points lies in the plane.
In creating the figure, we used Postulate 3 to determine the planes containing the three points on the left and the three points on the right. We used Postulate 1 to assign coordinates to the points on the line, and Postulate 2 to determine the lengths of the line segments. Finally, we used Postulate 4 to ensure that the lines connecting the points lie entirely in the planes that contain those points.
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Geometry Figure Postulates.
Here is a geometric figure containing points, lines, and planes:
o
|
|
o ----- o
/ \
/ \
o o
In this figure, there are three points labeled "o" and two lines connecting them. There are also two planes, one containing the three points on the left and one containing the three points on the right.
To create this figure, we used the following postulates:
In creating the figure, we used Postulate 3 to determine the planes containing the three points on the left and the three points on the right. We used Postulate 1 to assign coordinates to the points on the line, and Postulate 2 to determine the lengths of the line segments. Finally, we used Postulate 4 to ensure that the lines connecting the points lie entirely in the planes that contain those points.