Transcript Geometry: Chapter 2 - Hudson Falls Middle School

Geometry:
Chapter 2
By: Antonio Nassivera,
Dalton Hogan and Tom
Kiernan
Conditional Statements
A
conditional statement is an if-then
statement about two similar things.
 Ex. If it snows, then it is cold out.
 P->Q
 P= The hypothesis
 Q= The conclusion
Hypothesis
 The
hypothesis is the part after the word if.
 Conditional: If it snows, then it is cold out.
 The hypothesis of that statement would
be the “it snows” portion.
 The hypothesis is the P part of the
conditional statement “P->Q”.
Conclusion
 The
conclusion portion of an if-then
statement or conditional statement is the
part following the word then.
 Using the same conditional as before the
hypothesis was be the “it is cold out”
portion.
 The conclusion is the Q part of the
conditional statement that follows after
then.
Converse
A
converse switches the hypothesis and
conclusion order so it is Q->P not P->Q like
in a conditional statement.
 So if we were to use the same conditional
as before it would be: If it is cold out, then
it is snowing.
Inverse
 An
inverse, unlike a converse, negates the
hypothesis and conclusion of the
conditional statement instead of
switching their order.
 An inverse can be looked at as ~P->~Q
 Using the same conditional as before the
inverse of it would be: If it does not snow,
then it is not cold out.
Contrapositive




A contrapositive is a statement that switches
and negates the hypothesis and conclusion.
In other words it would be like making a
conditional statement be the converse and
the inverse at the same time.
It would look like ~Q->~P
Using the same conditional as the previous
ones it would be: If it is not snowing, then it is
not cold out.
Biconditional
A
biconditional is a statement that
connects the conditional and its converse
with if and only if.
 Symbol: P<->Q
 Ex. Conditional: If I eat, then I am hungry.
Converse: If I am hungry, then I eat.
Biconditional: I eat if and only if I am
hungry.
Law of Detachment
 If
a conditional is true and it’s hypothesis is
true then its conclusion is true.
 If P->Q and P are true statements then Q
is a true statement.
 Ex. If it is an A day, then I have gym.
Today is an A day. Therefore I have gym.
Law of Syllogism
 If
two conditionals are true then they can
be combined using the hypothesis from
the first conditional and the conclusion
from the second conditional.
 If P->Q and Q->R are true then P->R is true.
 If it is an A day, then I have gym. If I have
gym, then I can play sports. If it is an A
day, then I can play sports.
Properties
 Addition
property: If a=b then a+c=b+c
 Subtraction
property: If a=b then a–c=b-c
 Multiplication
 Division
property: If a=b then ac=bc
property: if a=b, and c does not
equal 0, then a/c=b/c
More Properties






Reflexive property: a=a or a is congruent to a
Symmetric property: If a=b then b=a. Or the
same but congruent, not equal
Transitive property: If a=b and b=c then a=c.
or the same but congreunt not equal.
Substitution property: If a=b then b can be
replace a in any equation.
Distributive property: a(b+c)=ab+ac
Angle Postulates/Theorems
 Vertical
 All
 If
angles are congruent.
right angles are congruent.
two angles are congruent and
supplementary then each angle is a right
angle.