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 a triangle has sides of lengths a, b, and c, what must be true?

Back

a + b > c, a + c > b, and b + c > a.

Front

Can a triangle have sides of lengths 3, 4, and 8?

Back

No, because 3 + 4 is not greater than 8.

Front

What is the minimum sum of the lengths of two sides of a triangle if the third side is 10?

Back

The sum must be greater than 10.

Front

If one side of a triangle is 5 and another is 7, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 and less than 12.

Front

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

Back

The segments will form a straight line, not a triangle.

Front

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

Back

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

Front

What is the relationship between the longest side and the sum of the other two sides in a triangle?

Back

The longest side must be less than the sum of the other two sides.

Front

Can a triangle have sides of lengths 1, 2, and 3?

Back

No, because 1 + 2 is not greater than 3.

Front

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

Back

It helps determine whether three given lengths can form a triangle.