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Rays - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

A ray is part of a line, has one fixed endpoint, and extends infinitely along the line from the endpoint. Opposite math rays are rays with a common endpoint, extending in opposite directions and forming a line.

If we had a line so it extends infinitely
in either direction, and I picked
an end point somewhere, and I erased everything
that extended beyond that
end point, what I've just
created is a ray.
So a ray has one end point and it extends
infinitely from that end point.

But how do you label a ray?
Well, you start off by saying
what is your end point?
My end point of this ray is A because that's
where it starts, and it extends
through point B. So I'm going to
label this ray A, B as a line but
I only have one arrow.
So the arrow is going
to be over the B.
Because my end point is A and notice I
do not have an arrow over the A, which
tells the geometry student or the geometry
teacher that this ray starts
at A and passes through B.

Now, you can also have opposite rays,
and opposite rays share
a common end point.
So if you look at this line right here,
containing X, Y and Z where X, Y and
Z are all co-linear.
We have opposite rays
if I pick point Y.
So I could say that the ray Y, Z -- so
again I'm saying from point Y through
point Z. So go YZ, and notice how
I level this where the arrow is
over the Z because it starts at Y and
the opposite one would be the ray
starting at Y passing
through X.
So I could label this as ray YX.

So opposite rays share an end point and
rays in general have one end point and
extend infinitely from
that end point.

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