Section 1.1: Getting Started (POINTS, LINES, RAYS, SEGMENTS, ANGLES, ETC.)
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Transcript of Section 1.1: Getting Started (POINTS, LINES, RAYS, SEGMENTS, ANGLES, ETC.)
SECTION 1.1: GETTING STARTED
(POINTS, LINES, RAYS, SEGMENTS,
ANGLES, ETC.)Allie Pusateri, Nicole Madensky,
and Brianna Benson
LINES Lines are made up of an infinite
number of points, are straight, and extend indefinitely far in both directions.
-- The line on the left is called line k.
-- The line in the middle can be called
-- The line on the right can be called line P
BC
AC
CB
CA
MN
NM
AB
BA
Not this
kind of
line!
LINE SEGMENTS Line segments are straight, made up of
points, and have a beginning and an end.
The segment on the left can be called or
The horizontal segment on the right can be called or
The other segment that is joined to the horizontal one through A can be called
or AN
AB BA
JL LJ
AN
RAYS Like lines and line segments, rays are
made up of points. However, a ray begins at an endpoint and
then extends indefinitely far in one direction.
The ray at the left can be called
The ray in the middle can be called
The ray at the right can be called
OW
SD
ME
MS
ET
ES
TS
TRIANGLES A triangle has three segments as its
sides. Those segments form three angles.
A triangle is named by its three endpoints.
This triangle can be called KDR, KRD, RDK, RKD, DKR, or DRK.
UNION AND INTERSECTION A triangle is a union (∪) of three segments. The intersection (∩) of any two sides of a
triangle is a vertex of the triangle.
The triangle is the union of three segments. DKR =
The intersection of any two sides is a vertex of the triangle = D
Try using colored
pencils to
determine the
union of segments,
lines, or rays.
KDKR DR
DR
DRKD
SAMPLE PROBLEMS
F a. How many lines are shown? b. Name these lines.
w c. Where do and intersect? d. ∩ = ?
e. = ?
ANSWERS: a. 2 b. line w, or ; or
c. F d. e.
D A L
a. Name the ray that has endpoint L and goes in the direction of D.
b. Name the segment joining A and L.
ANSWERS: a or
b. or
R K
PM
RP
KM
RP
FR
FM
MK
KM
RF
RP
FR
FP
PR
FM
MF
KF
FK
RP RFM
LA
LD
AL LA
PF
FP
SAMPLE PROBLEMS CONTINUED
Draw a diagram in which =ANSWER: F H G J
Draw a diagram in which GHI = L ANSWER: J * K
I H
*There are other correct answers.
FG HJ HG
G
KJ
L
EXPLANATION FOR SAMPLE PROBLEMS
1.a. There are two lines because a lines is made of many points and are straight.b. There are many names for these lines because you can name a line by any two points within it.c. They intersect at F because that's where they meet.d. This is where they overlap.e. This is because an angle is made of any two rays that meet at a common vertex.
2.a. There are two different answers to this because there are two points that have an endpoint L and go in the direction of D.b. The segment has two names because you can name a segment in any order.
3.a. To draw this diagram, you must be aware that they must overlap in order to form a segment.
4.a. They intersect at L because this is the point that the triangle and the ray meet.
PRACTICE PROBLEMS CONTINUED
= = ? = = ?
4.)
5.) Draw a diagram in which the intersection of and
is
XY
ZX XZ