Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Given three lengths, how can you determine if they can form a triangle?

Back

To determine if three lengths can form a triangle, check if the sum of the lengths of any two sides is greater than the length of the third side for all three combinations.

Front

If the lengths of the sides of a triangle are 6 cm, 6 cm, and 7 cm, do they satisfy the Triangle Inequality Theorem?

Back

Yes, they satisfy the Triangle Inequality Theorem because: 6 + 6 > 7, 6 + 7 > 6, and 6 + 7 > 6.

Front

Which of the following sets of lengths can represent the sides of a triangle: {28, 30, 58}?

Back

No, these lengths cannot represent the sides of a triangle because 28 + 30 is not greater than 58.

Front

Can the lengths 4 cm, 7 cm, and 10 cm form a triangle?

Back

Yes, they can form a triangle because 4 + 7 > 10, 4 + 10 > 7, and 7 + 10 > 4.

Front

What is an example of a set of lengths that cannot form a triangle?

Back

An example is {3 cm, 10 cm, 15 cm} because 3 + 10 is not greater than 15.

Front

What is the significance of the Triangle Inequality Theorem in geometry?

Back

The Triangle Inequality Theorem is significant because it provides a necessary condition for the existence of a triangle given three lengths.

Front

If a triangle has sides of lengths 3 ft, 5 ft, and 8 ft, can it exist?

Back

No, it cannot exist because 3 + 5 is not greater than 8.

Front

What is the first step in applying the Triangle Inequality Theorem?

Back

The first step is to identify the three lengths you want to test for forming a triangle.

Front

How do you express the Triangle Inequality Theorem mathematically?

Back

If a, b, and c are the lengths of the sides of a triangle, then a + b > c, a + c > b, and b + c > a must all hold true.