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It is often said that the shortest distance between two points is along the segment connecting them How does the Triangle Inequality Conjecture support this statement?
Wiki User
∙ 10y ago
First of all, it is true if the relevant metric is the Euclidean metric. However, for other metrics it need not be true.
The triangle inequality conjecture states that
|AC| + |CB| > |AB| for all C other than C = A or C = B
That is, the distance from A to B via any other point C is greater than along the line joining A to B.
Wiki User
∙ 10y ago
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What is a conjecture about the following statement triangle ABC has two equal angles?
One possible conjecture is that it has one median which coincides with the corresponding altitude.
What is the triangle sum conjecture?
triangle sum conjecture is the sum of the measures of the angles in every triangle is 180 degrees
What is isosceles triangle conjecture?
you too
If the connecting segment is neither horizontal or vertical you can form a right triangle and make the connecting segment the of the triangle?
hypotenuse
If the connecting segment is neither horizontal nor vertical you can form a triangle and make the connecting segment the hypotenuse of the triangle?
3
What is the statement of the triangle inequality theorem?
jizz in your mouth
What is a conjecture about the following statement triangle ABC has two equal angles?
One possible conjecture is that it has one median which coincides with the corresponding altitude.
What is the triangle sum conjecture?
triangle sum conjecture is the sum of the measures of the angles in every triangle is 180 degrees
Which of the following is the statement of the Triangle Inequality Theorem?
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
What does the shortest distance between them have to do with the triangle Inequality Conjecture?
The shortest distance between any two points, A and B, in a plane is the straight line joining them. Suppose, that the distance A to C and then C to B is shorter where C is any point not on AB. That would imply that, in triangle ABC, the sum of the lengths of two sides (AC and CB) is shorter tan the third side (AB). That contradicts the inequality conjecture.
What is isosceles triangle conjecture?
you too
What is the triangle inequality theorem?
It's the statement that in any triangle, the sum of the lengths of any two sides must be greater or equal to the length of the third side.
What is the Circumcenter Conjecture?
The circumcenter of a triangle is equidistant from the vertices.
What does the triangle inequality theorem state?
The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the other two sides.
What is an inverse statement of if a triangle is an equilateral triangle?
"if a triangle is an equilateral triangle" is a conditional clause, it is not a statement. There cannot be an inverse statement.
Can two sides be congruent in the triangle inequality?
no.
If the connecting segment is neither horizontal or vertical you can form a right triangle and make the connecting segment the of the triangle?
hypotenuse
