Question

In these triangles, the largest angle and the

largest side have been measured. What do
you notice?


The shortest distance between two points is a straight line.
It would obviously be shorter to walk distance c than to walk
a plus b. The Triangle Inequality says that a + b > c. What
other two inequalities could you write?

Answer 1

In these triangles, the largest angle and the largest side have been measured. This means that the two smaller sides and the two smaller angles are proportional to each other. This is known as the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. This means that the two smaller angles and the two smaller sides of the triangle must add up to be larger than the largest angle or side.

The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side. This means that two other inequalities can be written:

a > |c - b| and b > |c - a|,

where |x| is the absolute value of x. This means that the length of each side must be greater than the difference between the other two sides