Triangle Inequality

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

List the conditions for three lengths to form a triangle.

Back

The lengths a, b, and c can form a triangle if: a + b > c, a + c > b, and b + c > a.

Front

If the lengths of two sides of a triangle are 5 cm and 7 cm, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 cm and less than 12 cm.

Front

Can the lengths 3 cm, 4 cm, and 5 cm form a triangle?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

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

Back

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

Front

What is the minimum length of a side in a triangle if the other two sides are 8 cm and 10 cm?

Back

The minimum length must be greater than 2 cm (10 - 8).

Front

What is the maximum length of a side in a triangle if the other two sides are 6 cm and 9 cm?

Back

The maximum length can be less than 15 cm (6 + 9).

Front

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

Back

AC could be 16 inches, as it satisfies the triangle inequality.

Front

If the side lengths are 4 cm, 7 cm, and 10 cm, can they form a triangle?

Back

Yes, they can form a triangle.

Front

What is the relationship between the sides of a triangle and the angles opposite those sides?

Back

The larger the side length, the larger the angle opposite that side.