Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If two sides of a triangle are 27 and 39, what is the range for the length of the third side?

Back

The length of the third side must be between 12 and 66.

Front

If two sides of a triangle are 9 and 2, what is the range for the length of the third side?

Back

The length of the third side must be between 7 and 11.

Front

If two sides of a triangle are 10 and 10, what is the range for the length of the third side?

Back

The length of the third side must be between 0 and 20.

Front

What must be true about the sum of the lengths of any two sides of a triangle?

Back

The sum must be greater than the length of the third side.

Front

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

Back

No, they cannot form a triangle because 3 is not less than the sum of 2 and 1.

Front

What is the minimum possible length of the third side if the other two sides are 5 and 7?

Back

The minimum possible length of the third side is 3 (5 - 7).

Front

What is the maximum possible length of the third side if the other two sides are 5 and 7?

Back

The maximum possible length of the third side is 11 (5 + 7).

Front

If the lengths of two sides of a triangle are equal, what can be said about the third side?

Back

The third side must be less than the sum of the two equal sides and greater than the difference of the two equal sides.

Front

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

Back

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