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20 Cards in this Set
- Front
- Back
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If a>b and c>d,then a+c>b+d
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Addition property of inequalities
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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
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If a>b and b>c then a>c
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transitive property of inequalities
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If a=b+c and c>0 then a>b
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A property of inequalities
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The exterior angle inequality theorem
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The measure of an exterior angle of a triangle is > the measure of either interior angle
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Conditional statement
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if p then q
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Inverse of a conditional statement
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if not p then not q
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Contrapostive of a conditional statement
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If not q then not p
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venn diagram
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a circle diagram used to represent a conditional
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logically equivalent statement
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statements that are either both true or both false
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Summary of related if-then statements
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conditional: if p then q
contrapositive: If not q then not p converse: if q then p inverse: if not p then not q |
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indirect proof
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a proof in which it is temperarily assumed that the conclusion is false and then deduce a contradiction
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How to write an indirect proof
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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 |
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Complete: If one sides of a triangle is longer than a second side, then...
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the angle opposite the first side is larger than the angle opposite the second side
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Complete: If one angle of a triangle is larger than a second angle, then...
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the side opposite the first angle is loger than the side opposite the second angle
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Complete: The perpendicular segment from a point to a line...
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is the shortest segment from the point to the line
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Complete: The perpendicular segment from a point to a plane
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is the shortest segment from the point to the plane
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The sum of the lengths of any two sides of a triangle is greater than the length of the 3rd side
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Triangle inequality theorem
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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
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then the third side of the first triangle is longer than the third side of the second triangle
SAS Inequality Theorem |
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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
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then the included angle of the first triangle is larger than the included angle of the second.
SSS Inequality theorem |
