Triangle Inequality

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

Which of the following sets of lengths can form a triangle? 3, 6, 12; 7, 7, 14; 9, 9, 9; 13, 6, 7

Back

9, 9, 9

Front

If two sides of a triangle measure 5 and 10, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 5 and less than 15.

Front

What is the least possible integer length of the third side if two sides measure 57 and 32?

Back

26

Front

How do you determine if three lengths can form a triangle?

Back

Check if the sum of the lengths of any two sides is greater than the length of the third side for all combinations.

Front

If the sides of a triangle are 7 yd, 8 yd, and 9 yd, can they form a triangle?

Back

Yes, they can form a triangle.

Front

List the sides of a triangle with lengths 5, 12, and 13 from smallest to largest.

Back

5, 12, 13

Front

What is the maximum possible length of the third side if two sides measure 8 and 15?

Back

The maximum length of the third side is less than 23.

Front

If a triangle has sides measuring 10, 14, and x, what is the range of possible values for x?

Back

x must be greater than 4 and less than 24.

Front

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

Back

It helps to determine whether a set of lengths can form a triangle, which is fundamental in triangle construction and properties.