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

The following inequalities must hold: a + b > c, a + c > b, and b + c > a.

Front

Can the lengths 10, 17, and 16 form a triangle?

Back

Yes, because 10 + 16 > 17, 10 + 17 > 16, and 17 + 16 > 10.

Front

Can the lengths 2, 2, and 4 form a triangle?

Back

No, because 2 + 2 is not greater than 4.

Front

What is the maximum possible length of a side in a triangle with sides 10 and 17?

Back

The maximum possible length is less than 27 (10 + 17).

Front

What is the minimum possible length of a side in a triangle with sides 10 and 17?

Back

The minimum possible length is greater than 7 (17 - 10).

Front

If a triangle has sides of lengths 4, 7, and 10, what can be concluded?

Back

These lengths can form a triangle because they satisfy the triangle inequality.

Front

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

Back

Lengths 17, 9, and 30 cannot form a triangle because 17 + 9 is not greater than 30.

Front

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

Back

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

Front

What is the relationship between the sides of a triangle and its perimeter?

Back

The perimeter of a triangle is the sum of the lengths of all three sides.