Math Unit 10 Mrs. Lynch Proofs Unit

The Conditional Statement

p - q: If m<A is 35, then <A is an acute angle

The Converse

q - p: If <A is an acute angle, then m<A is 35

The Inverse

negative P - Negative Q: If M<A is NOT 35 then <A is NOT an acute angle

The ContraPositive

Negative Q - Negative P: If m<A is NOT an acute angle, Then <A is NOT 35.

Inductive Reasoning

Uses Patterns to make a conclusion

Deductive Reasoning

Uses Facts, Rules to come to a conclusion

Law of Detachment

If the hypothesis is true. Then the conclusion is true

Law of Syllogism

if P is equal to Q

And Q is Equal to R

Then P is equal to R

Reflexive Property

a = a

Symmetric Property

if a = b

then b = a

Transitive Property

If a = b

and b = c

then a = c

Segment Addition Property

AB + BC = AC

Angle Addition Property

<ABD + <DBC = <ABD

Mult Prop (=)

Multiplication

Given

It had been Given to you in the equation

Div Prop (=)

Division

Add Prop (=)

Addition

Biconditional Statement

1. Verify if the statement is true

2. P and if and only if Q

Example: The Converse is “If the sum of two angles is 90 degrees, then the angles are complementary” because this is true we can write the biconditional statement

Then the Biconditional statement would be the conditional statement but instead of if and then it would be if and only if

Biconditional statement: Two angles are complementary if and only if they are the sum of their measures is 90 degrees.