Triangle Inequality Flashcard

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 lengths are a, b, and c, what must be true for them to form a triangle?

Back

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

Front

Can a triangle be formed with side lengths 5, 7, and 12?

Back

No, because 5 + 7 is not greater than 12.

Front

What is the maximum possible length of a side in triangle ABC if AB = 10 inches and BC = 17 inches?

Back

The maximum length of side AC can be 26 inches (17 + 10 - 1).

Front

What is the minimum possible length of a side in triangle ABC if AB = 10 inches and BC = 17 inches?

Back

The minimum length of side AC can be 7 inches (17 - 10 + 1).

Front

Which of the following lengths cannot represent the sides of a triangle: 2, 3, 6?

Back

6 cannot represent the sides because 2 + 3 is not greater than 6.

Front

Can the lengths 4 cm, 7 cm, and 10 cm form a triangle?

Back

Yes, because 4 + 7 > 10, 4 + 10 > 7, and 7 + 10 > 4.

Front

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

Back

2, 2, and 4 cannot form a triangle because 2 + 2 is not greater than 4.

Front

If one side of a triangle is 10 inches, what is the range of possible lengths for the other two sides if they are both 5 inches?

Back

The lengths must satisfy 5 + 5 > 10, which is not true, so they cannot form a triangle.

Front

What is the significance of the Triangle Inequality Theorem in geometry?

Back

It helps determine whether three given lengths can form a triangle.