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 the side lengths of a triangle are a, b, and c, what must be true for these lengths to form a triangle?

Back

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

Front

Given side lengths of 5 and 7, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 (7 - 5) and less than 12 (5 + 7), so the range is (2, 12).

Front

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

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

Can the side lengths 3, 4, and 8 form a triangle?

Back

No, because 3 + 4 is not greater than 8.

Front

What is the smallest angle in a triangle with sides of lengths 6, 8, and 10?

Back

The smallest angle is opposite the shortest side, which is 6.

Front

If two sides of a triangle measure 10 and 14, what is the maximum possible length of the third side?

Back

The maximum possible length of the third side is 23 (10 + 14 - 1).

Front

What is the minimum possible length of the third side if the other two sides measure 10 and 14?

Back

The minimum possible length of the third side is 4 (14 - 10 + 1).

Front

How can you determine if three lengths can form a triangle?

Back

Use the Triangle Inequality Theorem: check if the sum of any two lengths is greater than the third length.

Front

What is the longest side in a triangle with angles measuring 30°, 60°, and 90°?

Back

The longest side is opposite the 90° angle.