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 two sides of a triangle are 5 and 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, so the range is 2 < x < 12.

Front

Can the lengths 3, 5, and 8 form a triangle?

Back

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

Front

What lengths cannot represent the sides of a triangle?

Back

If the lengths do not satisfy the Triangle Inequality Theorem, they cannot form a triangle.

Front

Given sides of lengths 12 and 7, what is the range for the third side?

Back

The range is 5 < x < 19.

Front

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

Back

The maximum length of the third side is 24, because 10 + 15 > x.

Front

What is the minimum length of the third side if the other two sides are 8 and 6?

Back

The minimum length of the third side is 3, because 8 - 6 < x.

Front

Can the lengths 9, 12, and 20 form a triangle?

Back

Yes, because 9 + 12 > 20.

Front

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

Back

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

Front

If the sides of a triangle are 4, 5, and x, what is the range for x?

Back

The range is 1 < x < 9.