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

Can a triangle be formed with side lengths 5, 10, and 15?

Back

No, because 5 + 10 is not greater than 15.

Front

Can a triangle be formed with side lengths 6, 8, and 10?

Back

Yes, because 6 + 8 > 10, 6 + 10 > 8, and 8 + 10 > 6.

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 two sides of a triangle are 7 cm and 10 cm, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 3 cm and less than 17 cm.

Front

What is the maximum length of a side in a triangle if the other two sides are 12 cm and 15 cm?

Back

The maximum length of the third side can be 26 cm (12 + 15 - 1).

Front

Can a triangle be formed with side lengths 3, 4, and 8?

Back

No, because 3 + 4 is not greater than 8.

Front

What is the minimum length of a side in a triangle if the other two sides are 5 cm and 7 cm?

Back

The minimum length of the third side must be greater than 2 cm (7 - 5).

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the length of AC?

Back

AC could be any length between 7 inches and 27 inches.

Front

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

Back

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