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20 Cards in this Set

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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 if-then 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