Transcript 5.2 Composite Argument and Linear Combination Properties

2.6 warm-up
If a is positive, b is negative, and c=0,
which of the following expression is
positive?
a. a(b+c)
b. c(a+b)
c. b(b-a+c)
d. c(a-b+ab)
10
2.6 warm-up
If a is positive, b is negative, and c=0,
which of the following expression is
positive?
a. a(b+c)
b. c(a+b)
c. b(b-a+c)
d. c(a-b+ab)
10
3.3 Parallel and
Perpendicular
Lines
You will use deductive reasoning to prove
a statement. You will also select an
appropriate representation in order to
solve problems.
Lets start off with some
theorems.
If two lines are parallel to the
same line, then they are
parallel to each other.
If a || b and b || c, then a || c.
a
b
c
Pardekooperu
Lets start off with some
theorems.
In a plane, if two lines are
perpendicular to the same
line, then they are parallel to
each other.
If a  b and b  c, then a || c
a
c
b
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.
If a || c and a  b, then b  c.
a
c
b
Lets try a problem.
Draw a picture and then form a conclusion
about line a and c.
ab
b || c
a
ac
Now
Look
write
at aa and c.
c
b
What
conditional
conclusion
statement.
can
be drawn ?
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 || b
b || c
c || d
a
b
c
a || d
d
Now
Look
at write
a andad. What conclusion can be drawn ?
If a || b, b ||statement.
c, and c || d, then a || d.
conditional
Assignment
Worksheet 3.3
Geometry
3.3 Parallel and Perpendicular Lines
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.
drawing:
drawing:
drawing:
conclusion:___________
conclusion:___________
conclusion:___________
conditional statement:
conditional statement:
conditional statement:
________________________
________________________
_____________________
________________________
________________________
_____________________
________________________
________________________
_____________________
a || b, b  c, c  d
drawing:
5.
a  b, b || c, c  d
drawing:
6.
a  b, b , c || d
drawing:
conclusion:___________
conclusion:___________
conclusion:___________
conditional statement:
conditional statement:
conditional statement:
________________________
________________________
_____________________
________________________
________________________
_____________________
________________________
________________________
_____________________
Pardekooper