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12 Cards in this Set
- Front
- Back
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The Exterior Angle Inequality Theorem
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The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle
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Inverse/contrapositive
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original- if p then q
Inverse- If not p, then not q Converse- if not q, then not p |
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Venn diagram
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Circle diagram
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logically equivalent
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statements that are either both true or both false
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How to write an indirect proof
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1. Assume temporarily that the conclusion is not true
2. Reason logically until you reach a contradiction of a known fact 3. Point out that the temporary assumption must be false and that the conclusion must then be true |
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Theorem
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If one side of a triangle is longer than a second side, then the angle oppostire the first side is larger than the angle opposite the second side
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Theorem
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If one angle of a triangle is larger than a second angle, then the side oppostire the first angle is longer than the side opposire the second angle
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Corollary
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The perpendicular segment from a point to a line is the shortest segment from the point to the line
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Corollary
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The perpendicular segment from a point to a plane is the shortest segment from the point to the plane
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Triangle Inequality Theorem
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THe sum of the lengths of any two sides of a triangle is greater than the length of the third side
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SAS Inequality Theorem
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if two triangles have 2 congruent sides but the included angle of one is larger than the other, then the third side of the larger one is longer than the third side of the smaller one
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SSS Inequality Theorem
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if two triangles have two congruent sides but the third side of one triangle is longer than the other, then the included angle of the larger triangle is larger than that of the smaller triangle
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