Triangle Inequality Theorem

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 two sides of a triangle are 7 ft and 13 ft, what is the range of possible lengths for the third side?

Back

The length of the third side must be more than 6 ft but less than 20 ft.

Front

Given side lengths of 4 and 12, what is the range of values for the third side?

Back

The length of the third side must be between 8 and 16.

Front

Can a triangle be formed with side lengths of 7 yd, 8 yd, and 9 yd?

Back

Yes, a triangle can be formed with these side lengths.

Front

Identify the shortest side in a triangle with sides QP, QM, and MP if QM is the shortest.

Back

QM is the shortest side.

Front

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

Back

The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

If one side of a triangle is 10 cm and another is 15 cm, what is the maximum length of the third side?

Back

The maximum length of the third side can be 24 cm (10 + 15 - 1).

Front

If the sides of a triangle are 5 cm, 12 cm, and x cm, what is the minimum value of x?

Back

The minimum value of x must be greater than 7 cm (12 - 5).

Front

What is the minimum length of a side in a triangle with sides 3 cm and 4 cm?

Back

The minimum length of the third side must be greater than 1 cm (4 - 3).

Front

In a triangle with sides 6 cm, 8 cm, and 10 cm, is it a right triangle?

Back

Yes, it is a right triangle because it satisfies the Pythagorean theorem (6^2 + 8^2 = 10^2).