Term
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Definition
If a > b and c ≥ d, then a + c > b + d
If a > b and c > 0, then ac > bc and a/c > b/c
If a > b and c < 0, then ac < bc and a/c < b/c
If a > b and b > c, then a > c
If a = b + c and c > 0, then a > b
Pg. 204 |
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Term
Theorem 6-1
The Ext. < Inequality
Theorem |
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Definition
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.
Pg. 204 |
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Term
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Definition
Given Statement: If p, then q
Contrapositive: If not q, then not p
Converse: If q, then p
Inverse: If not p, then not q
Pg. 208 |
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Term
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Definition
When the same venn diagram represents both a conditional and it contrapositive.
Pg. 208 |
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Term
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Definition
Begin by assuming temporarily that the desired conclusion is not true. Then you reason logically until you reach a contradiction of the hypothesis or some other known fact. Because you've reached a contradiction, you know that the temporary assumption is impossible and therefore the desired conclusion must be true.
Pg. 214 |
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Term
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Definition
If one side 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.
Pg. 219 |
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Term
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Definition
If one < of a triangle is larger than a second <, then the side opposite the first < is longer than the side opposite the second <.
Pg. 220 |
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Term
Corollary 1 and 2
of Theorem 6-3 |
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Definition
Corollary 1 - The perpendicular segment from a point to a line is the shortest segment from the point to the line.
Corollary 2 - The perpendicular segment from a point to a plane is the shoretest segment from the point to the plane.
Pg. 220 |
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Term
Theorem 6-4
The Triangle Inequality |
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Definition
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Pg. 220 |
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Term
Theorem 6-5
SAS Inequality Theorem |
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Definition
If two sides of one triangle are congruent to two sides of another triangle, but the included < of the first triangle is larger than the included < of te second, then the third side of the first triangle is longer than the third side of the second triangle.
Pg. 228 |
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Term
Theorem 6-6
SSS Inequality Theorem |
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Definition
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, then the included < of the first triangle is larger than the included < of the second.
Pg. 229 |
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