Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

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

Front

Can side lengths of 4, 4, and 4 form a triangle?

Back

True, because the sum of any two sides (4 + 4 = 8) is greater than the third side (4).

Front

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

Back

12, because 4 + 12 > 13 and 13 + 4 > 12.

Front

Given side lengths of 7 mm and 4 mm, what is the range for the third side?

Back

More than 3 mm but less than 11 mm.

Front

If a = 3 and b = 4, what is the possible length of c?

Back

5, because 3 + 4 > 5 and 3 + 5 > 4.

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the length of side AC?

Back

16 inches, because 10 + 16 > 17 and 17 + 10 > 16.

Front

What is the minimum length of the third side if two sides are 5 and 8?

Back

4, because 5 + 4 > 8.

Front

If one side of a triangle is 15 and the other is 10, what is the maximum length of the third side?

Back

24, because 15 + 10 > 24.

Front

What happens if the sum of two sides equals the third side?

Back

The three points are collinear, and they do not form a triangle.

Front

If the sides of a triangle are 6, 8, and 10, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 6 + 8 > 10, 6 + 10 > 8, and 8 + 10 > 6.