How can you prove inequalities of two triangles?

Triangle Inequality Proof Since the sum of any two sides is greater than the third, then the difference of any two sides will be less than the third. The sum of any two sides must be greater than the third side. The side opposite to a larger angle is the longest side in the triangle.

What is an example of a triangle inequality theorem?

Example 1: The sum of 7 and 9 is 16 and 16 is greater than 13 . The sum of 9 and 13 is 21 and 21 is greater than 7 . The sum of 7 and 13 is 20 and 20 is greater than 9 . This set of side lengths satisfies the Triangle Inequality Theorem.

How do you solve triangle inequalities?

According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than or equal to the third side of a triangle. This statement can symbolically be represented as; a + b > c. a + c > b.

What is proving inequalities in a triangle?

In geometry, the triangle inequality theorem states that when you add the lengths of any two sides of a triangle, their sum will be greater that the length of the third side.

What is triangle inequality proof?

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

How does triangle inequality theorem work?

triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

How does the figure help verify the triangle inequality theorem?

A by showing that a triangle cannot be formed when the sum of the lengths of two sides equals the length of the t d B. by showing that only one triangle can be formed when the sum of the lengths of two sides is less than the length the third C.

What is the triangle inequality formula?