Triangle Side Lengths Check

Front

Can the sides of a triangle have lengths 3, 4, and 9?

Back

No, because the sum of the lengths of the two shorter sides (3 + 4 = 7) must be greater than the length of the longest side (9).

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

What is a possible length of the rope in the given diagram if the other two sides are 10 and 12?

Back

The possible lengths must be between 2 and 22, but one possible length is 12.

Front

What is a possible third side to a triangle with side lengths of 13 and 4?

Back

12, because 4 + 13 > 12, 4 + 12 > 13, and 13 + 12 > 4.

Front

Does a triangle with these side lengths exist: 15, 12, 9?

Back

Yes, because 15 + 12 > 9, 15 + 9 > 12, and 12 + 9 > 15.

Front

What is a possible third side to a triangle with side lengths of 5 and 5?

Back

9, because 5 + 5 > 9 is not valid, but 5 + 9 > 5 and 5 + 9 > 5 are valid.

Front

If one side of a triangle is 7 and another is 10, what is the range of possible lengths for the third side?

Back

The third side must be greater than 3 and less than 17.

Front

What is the minimum length of the third side if two sides are 8 and 6?

Back

The minimum length is 3, because 8 + 6 > x must hold true.

Front

What happens if the sum of the two shorter sides equals the length of the longest side?

Back

The three points are collinear, and they do not form a triangle.

Front

Can a triangle have sides of lengths 2, 2, and 5?

Back

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