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

If the longest side of a triangle is 10, what must be true about the other two sides?

Back

The sum of the lengths of the other two sides must be greater than 10.

Front

Given sides a = 3 and b = 4, what is the maximum length of side c?

Back

The maximum length of side c can be 6 (3 + 4 - 1).

Front

Which of the following sets of numbers can represent the lengths of the sides of a triangle: {2,5,9}, {6,6,7}, {6,4,2}, {7,8,1}?

Back

{6,6,7} can represent the lengths of the sides of a triangle.

Front

What is a possible third side to a triangle with side lengths of 13 and 4?

Back

The possible third side can be 12.

Front

If two sides of a triangle are 2 and 6, which length cannot be the third side?

Back

The length 4 cannot be the third side.

Front

What is the minimum length of the third side if the other two sides are 5 and 7?

Back

The minimum length of the third side must be greater than 2 (5 - 7 + 1).

Front

If a triangle has sides of lengths 8, 15, and 17, does it satisfy the Triangle Inequality Theorem?

Back

Yes, it satisfies the Triangle Inequality Theorem because 8 + 15 > 17, 8 + 17 > 15, and 15 + 17 > 8.

Front

What is the relationship between the sides of a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

If one side of a triangle is 10, what is the range of possible lengths for the other two sides?

Back

The lengths of the other two sides must be greater than 10 when summed together.