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 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 must be greater than |10 - 17| = 7 inches and less than 10 + 17 = 27 inches. Possible lengths include 16 inches.

Front

Can the side lengths 3, 5, and 8 form a triangle?

Back

No, because 3 + 5 is not greater than 8.

Front

Which of the following sets of lengths cannot form a triangle: 2 cm, 6 cm, 7 cm, or 5 cm, 5 cm, 5 cm, or 8 cm, 3 cm, 10 cm, 15 cm?

Back

The lengths 3 cm, 10 cm, and 15 cm cannot form a triangle because 3 + 10 is not greater than 15.

Front

What are the conditions for three lengths to form a triangle?

Back

The lengths a, b, and c must satisfy: a + b > c, a + c > b, and b + c > a.

Front

If the sides of a triangle are 7, 7, and 7, what type of triangle is it?

Back

It is an equilateral triangle because all sides are equal.

Front

What is an example of side lengths that can form a triangle?

Back

The lengths 7, 9, and 10 can form a triangle because 7 + 9 > 10, 7 + 10 > 9, and 9 + 10 > 7.

Front

If one side of a triangle is 12 inches and the other is 5 inches, what is the range of possible lengths for the third side?

Back

The third side must be greater than |12 - 5| = 7 inches and less than 12 + 5 = 17 inches. Possible lengths are between 7 and 17 inches.

Front

What is the maximum length of a side in a triangle if the other two sides are 8 inches and 6 inches?

Back

The maximum length of the third side must be less than 8 + 6 = 14 inches.

Front

Can the lengths 4, 4, and 8 form a triangle?

Back

No, because 4 + 4 is not greater than 8.