Triangle Inequality Thm only

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

Can a triangle be formed with sides of lengths 15, 8, and 7?

Back

No, because 15 is not less than 8 + 7.

Front

If two sides of a triangle are 8 and 9, what is the range of possible lengths for the third side?

Back

1 < x < 17.

Front

Can a triangle be formed with sides of lengths 10, 9, and 2?

Back

Yes, because 10 < 9 + 2.

Front

If two sides of a triangle are 9 and 7, what is the range of possible lengths for the third side?

Back

2 < x < 16.

Front

What is the minimum length of the third side if two sides are 8 and 9?

Back

The minimum length is 1.

Front

What is the maximum length of the third side if two sides are 8 and 9?

Back

The maximum length is 17.

Front

Can a triangle be formed with sides of lengths 7, 6, and 12?

Back

Yes, because 7 + 6 > 12.

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 one side of a triangle is 10, and the other two sides are 5 and 6, can a triangle be formed?

Back

No, because 10 is not less than 5 + 6.