if a is positive, b is negative, and c=0, which of the following expression is positive? a. a(b+c)b....
TRANSCRIPT
If a is positive, b is negative, and c=0, If a is positive, b is negative, and c=0, which of the following expression is which of the following expression is positive?positive?
a.a. a(b+c)a(b+c) b. c(a+b)b. c(a+b)
c. b(b-a+c)c. b(b-a+c) d. c(a-b+ab) d. c(a-b+ab)
2.6 warm-up
10
If a is positive, b is negative, and c=0, If a is positive, b is negative, and c=0, which of the following expression is which of the following expression is positive?positive?
a.a. a(b+c)a(b+c) b. c(a+b)b. c(a+b)
c. b(b-a+c)c. b(b-a+c) d. c(a-b+ab) d. c(a-b+ab)
2.6 warm-up
10
3.3 Parallel and 3.3 Parallel and Perpendicular Perpendicular
LinesLines
You will use deductive reasoning to prove a statement. You will also select an
appropriate representation in order to solve problems.
Pardekooperu
Lets start off with some Lets start off with some theorems.theorems.
If two lines are parallel to the If two lines are parallel to the same line, then they are same line, then they are parallel to each other.parallel to each other.
aa
bb
cc
a || ba || b b || c,b || c,IfIf andand thenthen a || c.a || c.
Lets start off with some Lets start off with some theorems.theorems.
In a plane, if two lines are In a plane, if two lines are perpendicular to the same perpendicular to the same
line, then they are parallel to line, then they are parallel to each other.each other.
aa
bbcc
a a b b b b c, c,IfIf andand thenthen a a || || cc
One last theorems.One last theorems.In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular
to the other.
aa
bbcc
a a b, b, b b c. c.IfIf andand thenthena a || || cc
Lets try a problem.
Draw a picture and then form a conclusion about line a and c.
a ba
b
b || c
c
a c
Look at a and c. What conclusion can
be drawn ?
Now write a conditional statement.
If a b, and b || c, then a c.
Just one more.
Draw a picture and then form a conclusion about line a and d.
a || ba
b
b || c
c
c || d
d
Look at a and d. What conclusion can be drawn ?
a || d
Now write a conditional statement.If a || b, b || c, and c || d, then a || d.
AssignmentWorksheet 3.3
3.3 Parallel and Perpendicular Lines
PardekooperPardekooper
Geometry
Draw a picture for the following, form a conclusion about line a and d, and then write a conditional statement.1. a || b, b || c, c d 2. a || b, b c, c || d 3. a b, b || c. c || d
4. a || b, b c, c d 5. a b, b || c, c d 6. a b, b , c || d
drawing: drawing: drawing:
drawing: drawing: drawing:
conclusion:___________
conditional statement:
_____________________________________________________________________
conclusion:___________
conditional statement:
_____________________________________________________________________
conclusion:___________
conditional statement:
_____________________________________________________________________
conclusion:___________
conditional statement:
_____________________________________________________________________
conclusion:___________
conditional statement:
_____________________________________________________________________
conclusion:___________
conditional statement:
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