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

Can the side lengths 7 yd, 8 yd, and 9 yd form a triangle?

Back

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

Front

Can the side lengths 15 in., 12 in., and 2 in. form a triangle?

Back

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

Front

What is the range of values for the third side x if two sides are 4 and 12?

Back

The range is between 8 and 16.

Front

If a triangle has sides of lengths 5, 10, and x, what is the range of x?

Back

x must be between 5 and 15.

Front

What must be true for three lengths a, b, and c to form a triangle?

Back

a + b > c, a + c > b, and b + c > a must all be true.

Front

If one side of a triangle is 3 cm and the other is 4 cm, what is the maximum length of the third side?

Back

The maximum length of the third side is less than 7 cm.

Front

If a triangle has sides of lengths 6, 8, and 10, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 6 + 8 > 10, 6 + 10 > 8, and 8 + 10 > 6.

Front

What is an example of side lengths that cannot form a triangle?

Back

Side lengths 1, 2, and 3 cannot form a triangle because 1 + 2 is not greater than 3.

Front

What is the minimum length of the third side if two sides are 7 and 10?

Back

The minimum length of the third side is greater than 3.