We are asked to identify each figure as a line, a ray, a line segment, a point, or an
angle. Then name the figure using the given points.
Let's look at some definitions. A point has no length, no width and no height,
but it does have a location.
Here's an example of a point. Notice how it's labeled with the letter P. We
indicate this point by stating point P. A line is a set of points that extends
indefinitely in two directions.
Here's an example of a line, and notice the arrows on both ends indicating the set
of points extends indefinitely in both directions.
This line includes point A and point B. We indicate this line by stating line AB,
or writing the two letters A and B with a small line above the two letters.
Typically the letters are written in alphabetical order, although it would not be
wrong to state this line as line BA.
Going back to our question,
looking at the five figures. Notice how figure B is a point.
It's labeled with the letter Q and therefore, we indicate this point by stating
point Q. Looking at the remaining figures,
notice how figure E has arrows on both ends
indicating the set of points extends indefinitely in both directions. Figure E
is a line. The line contains the point P and the point Q. We indicate this line
by stating line PQ, or writing the letters P and Q with a small line above
the two letters.
Going back to our definitions. A line segment is a piece of a line with two
endpoints.
Here's an example of a segment. Notice how point A and point B of the two endpoints,
every segment has a specific length. Because the endpoints are point A
and point B, we indicate this segment by stating segment AB, or writing the
letters A and B with a small segment above the two letters. A ray is a part of a
line with the one endpoint. A ray extends indefinitely in one direction.
Here's an example of a ray. Notice it has one endpoint, point A. And because of the arrow
it extends indefinitely in this direction.
Also notice how the ray includes point B. We indicate this ray by stating ray AB, or
again point A is the endpoint, and point B is another point on the ray.
We can also indicate this ray by writing letters A and B with small ray above the
letters. So looking at the remaining figures, focusing on figure C and figure D, notice
figure C is a ray. It has one endpoint and extends in one direction indefinitely.
Because point B is the endpoint and the ray includes point F, we state this ray
as ray BF, or with the letters B and F with a small ray above the two letters.
Figure D has two endpoints and therefore, figure D is the segment.
Because the endpoints are point B and point C, we indicate this segment by stating segment BC, or
with the letters B and C with a small segment above the two letters.
So now we know the remaining figure is an angle. Let's review the definition of an
angle. An angle is made up of two rays that share a common endpoint. A common
endpoint is called the vertex.
Here's an example of an angle. This angle is made up of ray BC and ray BA. There
are several ways to indicate this angle, which is angle ABC. One way to state
this angle as angle ABC, or point B is the vertex. We can also state this angle as angle
CBA, again B the vertex. Using this notation, the vertex must always be in the middle.
Or we can state this as just using the vertex as angle B. And notice how there's a one
inside the angle, so we can also indicate this angle as angle one.
Notice how there's an arc here indicating the angle is the smaller
angle here. It's actually two angles formed by these two rays. This small angle and this
larger angle out here. So we should always include an arc when referring to an angle, so
we specifically know which angle it's being referred to.
We also can say that ray BA
and ray BC are the sides of the angle. Going back to our question.
Figure A is the angle.
Because point A is the vertex we indicate this angle by stating
angle DAE.
We could also say angle EAD, or using symbols we can say angle DAE,
or angle EAD.
Notice in each case, point A is the vertex.
I hope you found this helpful.