find a pattern for each sequence. use the pattern to show the next two terms or figures. 1)3, –6,...
TRANSCRIPT
Find a pattern for each sequence. Use the patternto show the next two terms or figures.
1) 3, –6, 18, –72, 3602)
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 1-2: (Do not write questions)
Warm-up Answers
1. -2160; 15,1202.
3. 554. Sample: 2 + 3 = 5, 2 and 3 are prime numbers but 5 is not even.
Practice 1-1 Answers
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.
Lesson 1-2: Points, Lines, & Planes
VocabTerm Definition Own Word
Point
Space
Line
Collinear
Plane
Coplanar
Postulate (axiom)
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.
Symbols• Point
• Line
• Plane
A
Point A
Plane M or plane ABC
AC
MB
SINGLE CAPITAL LETTER
SINGLE LOWER-CASE LETTER, OR
TWO CAPITAL LETTERS (POINTS) WITH LINE ABOVE
THREE CAPITAL LETTERS (any order)FROM POINTS ON PLANE (non-collinear, OR
ONE CAPITAL LETTER IN CORNER OF PLANE (NOT A POINT)
Line or AB or BAl
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.
lA
BC
AB, BC, or AC
2) Sketch a line that intersects a plane at one point.
SOLUTION Draw a plane and a line.
Emphasize the pointwhere they meet.
Dashes indicate wherethe line is hidden bythe plane.
3) What is the intersection of planes HGF and BCG?
A B
CD
E F
GH
How to draw a box:
Draw a rectangle for the front, and a rectangle for the back – connect the corners, make dashes where appropriate.
Hint: Shade the figures described in the directions.
Answer: line GF, or GFWhy is it a line? The figure represents planes which extend forever, so their intersection will extend forever – like a line.
Look for where the shaded regions touch!