geometry: chapter 6 Flashcards
Inverse
If not p then not q
Theorem 6-1: exterior angle inequality theorem
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle
Contra positive
If not q then not p
Logically equivalent
Conditional and contra positive
Given: if a then b
Contra positive:
Converse
Inverse
If not b then not a
If b then a
If not a then not b
How to write an indirect proof
1 assume temporarily that the conclusion is not true
2 reason logically until you reach a contradiction of the known fact
Theorem 6-2
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
Theorem 6-3
If one angle of a triangle is larger than a second angle then the side opposite the first angle is longer than the side opposite the second angle
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 shortest segment from the point to the plane
Theorem 6-4 the triangle inequality
The some of the links of any two side of a triangle is greater than the length of the third side
Theorem 6-5 SAS inequality theorem
If two sides of one triangle are congruent to two sides of another triangle but the included angle of the first triangle is larger than the included angle of the second and the third side of the first triangle is longer than the third side of the second triangle
Theorem 6-6 SSS 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 and the included angle of the first triangle is larger than the included angle of the second
