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

Will the sides 3, 4, and 5 form a triangle?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

What is the range of possible lengths for the third side of a triangle with sides measuring 7 ft and 13 ft?

Back

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

Front

If side AB is 10 inches and side BC is 17 inches, what could be the length of side AC?

Back

The length of side AC could be 16 inches.

Front

Will the segments 2, 2, and 5 form a triangle?

Back

No, because 2 + 2 is not greater than 5.

Front

Identify the shortest side in triangle QPM with sides QP, QM, and MP.

Back

The shortest side is QM.

Front

What is the minimum length for the third side of a triangle if the other two sides are 8 and 10?

Back

The minimum length for the third side is 3 (8 + 3 > 10).

Front

What is the maximum length for the third side of a triangle if the other two sides are 5 and 12?

Back

The maximum length for the third side is 16 (5 + 12 > 16).

Front

If two sides of a triangle are 6 cm and 9 cm, what is the range for the third side?

Back

The third side must be more than 3 cm but less than 15 cm.

Front

Can the sides 1, 2, and 3 form a triangle?

Back

No, because 1 + 2 is not greater than 3.