Triangle Inequality Theorem (Ordering and Forming Triangles)

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

Given sides a, b, and c, how can you determine if a triangle can be formed?

Back

A triangle can be formed if the following conditions are met: a + b > c, a + c > b, and b + c > a.

Front

If side lengths are 10 inches and 17 inches, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 7 inches and less than 27 inches (10 + 17 > AC > |10 - 17|).

Front

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

Back

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

Front

How do you identify the shortest side in a triangle given the side lengths?

Back

The shortest side is the one with the smallest numerical value among the three side lengths.

Front

How do you list the angles of a triangle in order from smallest to largest?

Back

To list the angles from smallest to largest, compare the lengths of the sides opposite each angle; the angle opposite the shortest side is the smallest.

Front

What is the significance of the longest side in a triangle?

Back

The longest side of a triangle is crucial for determining the triangle's shape and is always opposite the largest angle.

Front

Can a triangle be formed with side lengths of 15 in., 12 in., and 2 in.?

Back

No, a triangle cannot be formed with these side lengths because 15 + 12 is not greater than 2.

Front

What is the formula to find the range of possible lengths for the third side of a triangle?

Back

The range for the third side length (c) can be found using: |a - b| < c < a + b.

Front

What is the definition of a scalene triangle?

Back

A scalene triangle is a triangle in which all three sides have different lengths.