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

If two sides of a triangle are 8 and 15, what is the range of possible lengths for the third side?

Back

7 < x < 23

Front

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

Back

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

Front

What is the minimum length of the third side if two sides are 7 and 10?

Back

The minimum length is 4 (10 - 7).

Front

What is the maximum length of the third side if two sides are 7 and 10?

Back

The maximum length is 16 (7 + 10).

Front

If a triangle has sides of lengths 6, 8, and 10, can it be formed?

Back

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

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 the sides of a triangle are 3, 4, and 5, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem.

Front

What is the sum of the angles in any triangle?

Back

The sum of the angles in any triangle is always 180 degrees.

Front

Can a triangle be formed with side lengths 2, 2, and 5?

Back

No, because 2 + 2 is not greater than 5.