Geometry: Chapter 2By: 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 property: If a=b then ac=bc

Division 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 angles are congruent.

All right angles are congruent.

If two angles are congruent and supplementary then each angle is a right angle.