geometry lesson 1.2 points, lines, and planes · geometry lesson 1.2 points, lines, and planes...
TRANSCRIPT
Objectives
� Students will be able to:
� Define: Point, line, plane, collinear, coplanar, line segment, ray, intersect, intersection
� Name collinear and coplanar points
� Draw lines, line segments, and rays with proper labeling
� Draw opposite rays
� Sketch intersections of lines and planes and two planes
Warm-Up: Common Words
�What are “common words” we use in
everyday conversation?
� Do you have to think about their
meaning?
�What if you didn’t know these words?
� In today’s lesson you will learn about
common words needed to speak the
language of geometry
Warm-Up Activity: Points & Lines� Mark the intersection of Hayden and
McDonald
� Mark the intersection of Hayden and Indian Bend
� Mark the intersection of Hayden and Jackrabbit
� What appears to be true of the dots you
made?
•Mark the intersection of
Hayden and McDonald
•Mark the intersection of
Hayden and Indian Bend
•Mark the intersection of
Hayden and Jackrabbit
•What appears to be true of
the dots you made?
1A. Points, Lines, and Planes
A location in space, but has no size or shape
AB Extends without end in
one dimension (two directions) and always
straightCalled ABor line l
AB
C
Extends without end in
two dimensions (all
directions), always flat, and has no thickness
Calledplane ABCor plane M
Called
point A
M
l
1B. Collinear and Coplanar
Points on the same line
Points
Points or Lines
Points on the same plane
D E F G
A B C
“Co” means “together”
D, E, F, and G are collinear
A, B, and C are coplanar pointsLines l and n are coplanar lines
l
n
Example 1: Naming Points
� Three points that
are collinear:
� Four points that
are coplanar:
� Three points that
are not collinear:
DE F
G
H
D, E, F
D, E, F, G and D, E, F, H (plane not shown)
H, E, G
Practice 1A: Naming Points
� Name a point that is collinear with the
given points
� B and E:
�C and H:
� D and G:
� A and C:
� H and E:
�G and B:
I
E
B
B
C
D
Practice 1B: Naming Points
� Name a point that is coplanar with the
given points
�M, N, R:
�M, N, O:
�M, T, Q:
�Q, T, R:
� T, R, S:
�Q, S, O:
T
P
P
S
Q
P
2. Line Segments and Rays
End points A and B and all
points in between
A B
A B
Line AB
Line segment AB
Starting point and all points on
one side of the starting point
A BRay AB
AB
AB
A BRay BA BA
AB
Example 2: Drawing Lines & Rays
� Draw points J, K, and L (non-collinear)
� Then, draw JK, KL, and LJ
J
K
L
Practice 2: Drawing Lines & Rays
� Draw three collinear points A, B, and C
� Draw a point D that is non-collinear with A,
B, and C
� Draw AB
� Draw BD
� Draw CD
3. Intersections
Two figures having one or
more points in common
The set of points the two figures have in
common
Lines k and l have point
A in common, so point A
is the intersection
Ak
l
(verb)
(noun)
Activity: Questions 1-4
1. When the cards are NOT together:
What is the intersection of AB and
CD? AB and EF?
2. With the cards together, what is the
intersection of CD and EF?
3. What is the intersection of planes M
and N?
4. Are CD and EF coplanar? Explain.
Point G Point G
Point G
AB
Yes, these two intersecting lines form a plane