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20 Cards in this Set
 Front
 Back
If a>b and c>d,then a+c>b+d

Addition property of inequalities


If a>b and c>0 then ac>bc and a/c>b/c
or If a>b and c<0 then ac< bc and a/c<b/c 
multiplication property of inequalities


If a>b and b>c then a>c

transitive property of inequalities


If a=b+c and c>0 then a>b

A property of inequalities


The exterior angle inequality theorem

The measure of an exterior angle of a triangle is > the measure of either interior angle


Conditional statement

if p then q


Inverse of a conditional statement

if not p then not q


Contrapostive of a conditional statement

If not q then not p


venn diagram

a circle diagram used to represent a conditional


logically equivalent statement

statements that are either both true or both false


Summary of related ifthen statements

conditional: if p then q
contrapositive: If not q then not p converse: if q then p inverse: if not p then not q 

indirect proof

a proof in which it is temperarily assumed that the conclusion is false and then deduce a contradiction


How to write an indirect proof

1. Assume temperarily that the conclusion is false
2. reason logically until you reach a contradiction 3. point our the the temporary assumption must be false and that the conclusion must then be true 

Complete: If one sides of a triangle is longer than a second side, then...

the angle opposite the first side is larger than the angle opposite the second side


Complete: If one angle of a triangle is larger than a second angle, then...

the side opposite the first angle is loger than the side opposite the second angle


Complete: The perpendicular segment from a point to a line...

is the shortest segment from the point to the line


Complete: The perpendicular segment from a point to a plane

is the shortest segment from the point to the plane


The sum of the lengths of any two sides of a triangle is greater than the length of the 3rd side

Triangle inequality theorem


If two sides of one triangle are congruent to two sides of another triangle, but the included angle of one triangle is larger than the included angle of the second

then the third side of the first triangle is longer than the third side of the second triangle
SAS Inequality Theorem 

If two sides of one triangle are congruent to two sides of another triangle but the third side of the first triangle is longer than the third side of the second triangle

then the included angle of the first triangle is larger than the included angle of the second.
SSS Inequality theorem 