geometry postulates and rules

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all of the postulates and rules

postulate 1-1

through any two points there is exactly one line

postulate 1-2

if two distinct lines intersect, then they intersect in exactly one point

postulate 1-3

if two distinct planes intersect, then they intersect in exactly one line

postulate 1-4

through any three noncollinear points, there is exactly one plane

what happens if three points are collinear?

there are an infinite amount of planes

why are there an infinite amount of planes when there are three points?

because you can rotate the plane on the line in any direction to form an unlimited amount of planes

how many planes contain a given line...why?

infinitely many because a plane can rotate on the line in any direction forming an unlimited amount of planes

can a plane have an endpoint?

no it always extends in all directions

by its endpoint

what does coplanar mean?

points and lines that lie on the same plane

what does collinear mean?

points that lie on the same line

suppose two points are in plane P. Explain why the line containing the points is also in plan P

because for every two points there is one line, if two points of a line are in plane P, that means that all of the points of the line and the line are in plane P

what is a net?

a two dimensional diagram that you can fold to form a three-dimensional figure

what is an orthographic drawing?

another way to represent a three-dimensional figure

when do you put the dashed line in an orthographic drawing??

to show hidden edges

a rectangle

2 ways

if you are given a line segment with A B C, the midpoint is B, what does that tell you about A and C?

that they are the same value

if you are given a midpoint problem with A B and C what do you do to solve it? ( A and C contain variables)

you set AB to equal BC and find the value of the variable and plug it back into both AB and BC then add them together to find the value of AC

how do you find the length of segments?

by subtracting then finding the absolute value

a segment

what are opposite rays?

two rays that share the same endpoint

what is the ruler postulate?

every point on a line can be paired with a coordinate

what is the segment addition postulate?

if 3 points A B and C are collinear, and B is between A and C, then AB + BC= AC

midpoint

segment bisector

how do you describe a plane?

by the 3 noncollinear points in it

how many lines does a plane contain?

infinitely many lines

coplanar

why are intersecting lines always coplanar?

because 2 points lie on each of the two lines, and if two points of a line are in the plane, then all the points of the line and the line are in the plane

what do solid lines show in an orthographic drawing?

show visible edges

Example: