Transcript Lesson 1-2: Points, Lines, & Planes

Warm-up 1-2: (Do not write questions
Find a pattern for each sequence. Use the pattern
to show the next two terms or figures.
1)
2)
3, –6, 18, –72, 360
Make a table of the sum of the first 4 counting numbers. Use
your table and inductive reasoning to find the following:
3)
the sum of the first 10 counting numbers
Show that the conjecture is false by finding one counterexample.
4)
The sum of two prime numbers is an even number.
Warm-up Answers
1. -2160; 15,120
2.
3. 55
4. Sample: 2 + 3 = 5, 2 and 3 are prime numbers
but 5 is not even.
Practice 1-1 Answers
Lesson 1-2: Points, Lines, & Planes
Objectives: (Do not write)
• Students will identify and correctly name points lines and
planes
• Students will recognize the shapes formed by the
intersection of lines and planes.
Vocab
Term
Point
Space
Line
Collinear
Plane
Coplanar
Postulate
(axiom)
Definition
A location
The set of all points in
all directions
A series of points that
extend in 2 opposite
directions
Points that lie on the
same line.
A flat surface that
extends forever.
Points or lines that lie
in the same plane.
A statement accepted
as a fact.
Own Word
Symbols
• Point
Point A
SINGLE CAPITAL LETTER
A
Line
or AB
or BA
• Line l
• Plane
SINGLE LOWER-CASE
LETTER, OR
TWO CAPITAL LETTERS
(POINTS) WITH LINE
ABOVE
A
B
C
M
Plane M or plane ABC
THREE CAPITAL LETTERS
(any order)FROM POINTS
ON PLANE (non-collinear,
OR
ONE CAPITAL LETTER IN
CORNER OF PLANE (NOT A
POINT)
Postulates (axioms)
1) Through any two points there is exactly one
line
2) When two lines intersect, they form exactly
one point
3) When two planes intersect they form exactly
one line
(Try drawing them to see…)
In Class Examples
1) Draw line l. Create 3 collinear points A,
B, C on line l. Then name line l in three
other ways.
C
B
A
AB, BC, or AC
l
2) Sketch a line that intersects a plane at one point.
SOLUTION
Draw a plane and a line.
Emphasize the point
where they meet.
Dashes indicate where
the line is hidden by
the plane.
3) What is the intersection of planes HGF and BCG?
How to draw a box:
Draw a rectangle for
the front, and a
rectangle for the back
– connect the
corners, make dashes
where appropriate.
H
E
G
Hint: Shade the
figures described in
the directions.
F
D
A
C
Look for where
the shaded
regions touch!
B
Answer: line GF, or GF
Why is it a line? The figure represents planes which extend forever, so their
intersection will extend forever – like a line.