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 the side lengths of a triangle are 7 yd, 8 yd, and 9 yd, can a triangle be formed?

Back

Yes, because 7 + 8 > 9, 7 + 9 > 8, and 8 + 9 > 7.

Front

Can a triangle be formed with side lengths 0, 11, and 12?

Back

No, because one side length is zero, which does not satisfy the Triangle Inequality Theorem.

Front

Determine if a triangle can be formed with side lengths 15 in., 12 in., and 2 in.

Back

No, because 15 + 12 is not greater than 2.

Front

Which set of side lengths can form a triangle: 3, 6, 12; 7, 7, 14; 9, 9, 9; 13, 6, 7?

Back

9, 9, 9 can form a triangle because 9 + 9 > 9.

Front

Identify the lengths that cannot represent the sides of a triangle: 32, 34, 60, 28, 30, 58, 13, 20, 27, 2, 4, 5.

Back

28, 30, and 58 cannot represent the sides of a triangle.

Front

What is the condition for three lengths a, b, and c to form a triangle?

Back

The conditions are: a + b > c, a + c > b, and b + c > a.

Front

If a triangle has sides of lengths 5, 12, and 13, can it be formed?

Back

Yes, because 5 + 12 > 13, 5 + 13 > 12, and 12 + 13 > 5.

Front

What happens if one side of a triangle is equal to the sum of the other two sides?

Back

A triangle cannot be formed; it will be a straight line.

Front

Can a triangle be formed with side lengths 10, 6, and 5?

Back

Yes, because 10 + 6 > 5, 10 + 5 > 6, and 6 + 5 > 10.