Warm-up
7
Solve:
14x = 2(5x + 14)
Ch 2 Preview
• LOGIC!
(determine the truth values of statements
and justify conjectures)
– Conditionals & their converses
– Algebraic Properties
• Geometry
– Congruence Properties
– Vertical Angles
2-1
Conditional
Statements
You will be able to recognize
conditional statements and write
their converses.
A conditional is an
if-then statement.
The hypothesis follows if.
The conclusion follows
then.
How many letters follow the “s” in
conclusion?
a. Identify the hyp. & conc.:
If y – 3 = 5, then y = 8.
hyp: y – 3 = 5, conc: y = 8
Note: If & then are not part of the
hyp. or conc.
Identify the hyp. & conc.:
y = 8 if y – 3 = 5.
hyp: y – 3 = 5, conc: y = 8
b. Write the sentence as a
conditional:
A square has four cong. sides.
If a figure is a square, then it
has four cong. sides.
Hint: Use the verb to help
separate the hyp from the conc.
Note: Do not start a conditional
with it or they.
c. Write the sentence as a
conditional:
An integer that ends with 0 is
divisible by 5.
If an integer ends with 0, then it
is divisible by 5.
The truth value can be T or F.
For true:
show that every time the hyp.
is true, the conc. is true.
For false:
find one counterexample for
which the hyp. is true and the
conc. is false.
d. Show the cond. is false:
If the month is February, then
there are only 28 days in the
month.
February during a leap year
has 29 days.
Using a Venn Diagram:
the set that satisfies the hyp
lies inside the set that satisfies
the conc.
Dogs
e. Draw a Venn:
If an animal is a
Cocker
cocker spaniel,
Spaniels
then it is a dog.
A converse switches the
hypothesis and conclusion.
conditional: p → q
If p, then q.
converse: q → p
If q, then p.
f. Write the converse:
If two lines are not parallel and
do not intersect
intersect, then they are
skew.
skew
theylines
are skew
If two
are skew, then
they are not parallel and do
not intersect.
True or False? True
g. Write the conv. and
determine the truth value of the
cond. and the conv.:
If two lines do not intersect,
then they are parallel.
If two lines are parallel, then they
do not intersect.
Cond: False
Conv: True
h. Write the conv. and
determine the truth value of the
cond. and the conv.:
If x = 2, then |x| = 2.
If |x| = 2, then x = 2.
Cond: True
Conv: False
2-1 p. 71-74
#5-33 e.o.o.*,
46, 52-58 even, 59-61
*every other odd