If I get a 100%, then I will have
an A.
What is p?
I get a 100%
What is q?
I will have an A
What is the converse?
If I have an A, then I got a 100%.
If I get a 100%, then I will have
an A.
What is the inverse?
If I don’t get a 100%, then I won’t have an A.
What is the contrapositive?
If I don’t have an A, then I didn’t get a 100%
Is the inverse true or false?
False, I could get a 98% and still have an A.
Five times an angle’s supplement is 132
more than the angle. Find the measure
of the angle.
5(180 – x) = x + 132
900 – 5x = x + 132
768 = 6x
128 = x
How do you know that:
8
1
7
2
Angle 8 is congruent to angle 2?
Vertical angle thm
Angle 1 is supplementary to angle 2?
Definition of a linear pair
Angle 7 congruent to angle 1?
Vertical angle thm
Construct a truth table for (pV~q)Λr
p
q
~q
(pV~q)
r
T
T
T
T
F
T
F
F
T
F
T
F
F
F
F
T
T
T
T
F
F
T
T
T
T
F
F
T
T
F
F
T
T
F
T
F
T
F
T
F
(pV~q)Λr
T
F
T
F
F
F
T
F
If an animal is a zebra, then it is
mammal.
What is the inverse?
If an animal is NOT a zebra, then it is not a mammal.
What is the contrapositive?
If an animal is not a mammal, then it is not a zebra.
Is the inverse true or false?
False, the mammal could be a human.
If an animal is a zebra, then it is
mammal.
What is p?
An animal is a zebra
What is q?
It is a mammal
What is the converse?
If an animal is a mammal, then it is a zebra.
How do you know that:
E
A
F
B
C
Angle E is a right angle?
Given
Angle E is congruent to angle EBC?
Right angle thm
Angle ABC is a straight angle?
Assumed from diagram.
D
How do you know that:
E
A
F
B
D
C
Angle ABC is congruent to angle EFD?
If 2 angles are straight angles, then they are congruent
Segment EF + segment FD = segment ED?
Segment addition postulate
Angle ABE + angle EBC = 180?
Definition of linear pair.
Construct a truth table for (~p ᴠ q)ᴠ~r
p
~p
q
T
F
F
F
F
T
T
T
T
T
T
T
T
F
F
F
F
T
F
F
T
T
F
F
(~pVq)
T
T
F
F
T
T
T
T
r
~r
T
F
T
F
T
F
T
F
T
F
T
F
T
F
T
F
(~pVq)V~r
T
T
F
T
T
T
T
T
How do you know that:
E
A
F
B
Given: B is the midpoint of segment AC
F is the midpoint of segment ED
BC is congruent to EF
EF congruent to FD?
Definition of midpoint
FD congruent to BC?
Transitive property
C
D
How do you know that:
E
A
F
B
Given: B is the midpoint of segment AC
F is the midpoint of segment ED
BC is congruent to EF
D
C
ED congruent to AC?
Like multiples of congruent segments are congruent
F is the midpoint of segment ED?
Given
The sum of twice an angle and its complement
is 50 less than the angle’s supplement. Find
the measure of the angle’s complement.
2x + 90 – x = 180 – x – 50
x + 90 = -x + 130
2x = 40
x = 20
complement = 70˚
Write as a biconditional:
An octagon is a polygon with 8 sides.
A polygon is an octagon iff it has 8 sides.
How do you know that:
Given: B is the midpoint of segment AC
A
B
C
B is the midpoint of segment AC?
Given
AB + BC = AC?
Segment addition postulate
AB = BC?
Definition of midpoint
If a polygon is a triangle, then
it has 3 sides.
a) Identify p and q
b) Is the converse
true or false?
True (definition!)
If a polygon is a triangle, then
it has 3 sides.
a) What is the inverse?
If a polygon is not a triangle, then it
does not have 3 sides.
b) What is the conclusion?
it has 3 sides.
How do you know that:
C
D
H
4
1
2
B
Given: AH and FG are angle bisectors
Angle 1 congruent to angle 3
A
F
G
3
E
Angle 1 congruent to angle 2?
Definition of angle bisector
Angle CAB congruent to angle DFE?
Like multiples of congruent angles are congruent
Construct a truth table for (pΛ~q)ᴠr .
p
q
~q
T
T
T
T
T
F
T
F
F
T
F
T
F
F
F
F
F
F
T
T
F
F
T
T
(pΛ~q)
F
F
T
T
F
F
F
F
r
T
F
T
F
T
F
T
F
(pΛ~q)Vr
T
F
T
T
T
F
T
F
How do you know that:
D
C
H
1
A
2
4
B
Given: Angle CAB congruent to angle DFE
angle 1 congruent to angle 4
F
G
3
E
Angle 3 congruent to angle 2?
Subtraction—when congruent angles are subtracted
from congruent angles, the differences are
congruent.
Angle 1 + angle 2 = angle CAB?
Angle addition postulate