4.7 Triangle Inequalities

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

Does a triangle with side lengths 15, 12, and 9 exist?

Back

Yes, because 15 + 12 > 9, 15 + 9 > 12, and 12 + 9 > 15.

Front

Can the sides of a triangle have lengths 4, 11, and 13?

Back

Yes, because 4 + 11 > 13, 4 + 13 > 11, and 11 + 13 > 4.

Front

What is a possible third side to a triangle with side lengths of 13 and 4?

Back

12, because 4 + 12 > 13 and 13 + 4 > 12.

Front

In a triangle, if m∠B=45° and m∠C=55°, what is the order of the sides in length from longest to shortest?

Back

BC, AB, AC, because the largest angle is opposite the longest side.

Front

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

Back

In a triangle, the larger the angle, the longer the side opposite that angle.

Front

What is the largest angle in a triangle with angles ∠D, ∠E, and ∠F?

Back

∠E, if it is the largest angle among the three.

Front

If a triangle has sides of lengths 7, 10, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 7 + 5 > 10, 7 + 10 > 5, and 10 + 5 > 7.

Front

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

Back

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

Front

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

Back

The maximum length can be less than 18 (8 + 10).