Triangle Inequality Theorem (Ordering and Forming Triangles)

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 10 inches and 17 inches, what could be the length of the third side?

Back

The length of the third side must be greater than 7 inches and less than 27 inches.

Front

Given two sides of lengths 7 ft and 13 ft, what is the range for the third side?

Back

The third side must be more than 6 ft but less than 20 ft.

Front

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

Back

Only the set 9, 9, 9 can form a triangle.

Front

What is the shortest side in a triangle with sides QP, QM, MP if QM is 5 inches, QP is 8 inches, and MP is 10 inches?

Back

QM is the shortest side.

Front

Can a triangle be formed with side lengths 15 in., 12 in., and 2 in.?

Back

No, a triangle cannot be formed with these lengths.

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 one side of a triangle is 10 cm and the other is 5 cm, what is the maximum length of the third side?

Back

The maximum length of the third side is less than 15 cm.

Front

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

Back

The minimum length of the third side is greater than 2 cm.

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, what is the possible range for AC?

Back

AC must be greater than 7 inches and less than 27 inches.