through any two points there is exactly one line
if two distinct lines intersect, then they intersect in exactly one point
if two distinct planes intersect, then they intersect in exactly one line
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
how do you name a ray?
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
if you were to form a net of a cylinder, what would the shape in the middle be??
how many ways can you fold a tetrahedron?( a shape with 4 triangles including the base)
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
part of a line that consists of two endpoints and all the points between them
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
a point that divides a segment into two congruent segments
a point, line, or ray that intersects a segment at its midpoint
how do you describe a plane?
by the 3 noncollinear points in it
how many lines does a plane contain?
infinitely many lines
intersecting lines are always...
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