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 the sides of a triangle are 7 yd, 8 yd, and 9 yd, can they form a triangle?

Back

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

Front

If the longest side of a triangle is 10, what must be true about the other two sides?

Back

The sum of the lengths of the other two sides must be greater than 10.

Front

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

Back

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

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 lengths cannot represent the sides of a triangle: 32, 34, 60, 28, 30, 58, 13, 20, 27, 2, 4, 5?

Back

28, 30, and 58 cannot represent the sides of a triangle.

Front

What is the minimum requirement for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

If a triangle has sides of lengths 5, 7, and x, what must x be for the triangle to exist?

Back

x must be greater than 2 and less than 12 (2 < x < 12).

Front

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

Back

Example: 6, 8, and 10 can form a triangle because 6 + 8 > 10.

Front

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

Back

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