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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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Definition
Given Statement: If p, then q.
End Statement: If not q, then not p. |
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Definition
Given Statement: If p, then q.
End Statement: If q, then p. |
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| Summary of Related If-Then Statements |
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Definition
Given Statement: If p, then q.
Inverse: If not p, then not q.
Converse: If q, then p.
Contrapositive: If not q, then not p.
*A statement and its contrapositive are logically equivalent.
*A statement is not logically equivalent to its converse or to its inverse. |
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| How to Write an Indirect Proof |
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Definition
1. Assume temporarily that the conslusion 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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| If one side of a triangle is longer than a second side, |
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Definition
| then the angle opposite the first side is larger than the angle opposite the second side. |
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| If one angle of a triangle is larger than a second angle, |
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Definition
| then the side opposite the first angle is longer than the side opposite the second angle. |
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| The perpendicular segment from a point to a line is... |
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Definition
| the shortest segment from the point to the line |
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| The perpendicular segment from a point to a plane is... |
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| the shortest segment from the point to the plane. |
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| Triangle Inequality Theorem |
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Definition
| The sum of the length of any two sides of a triangle is greater than the length of the third side. |
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