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 a triangle has sides of lengths a, b, and c, what must be true?

Back

a + b > c, a + c > b, and b + c > a.

Front

List the side measures of a triangle in order from shortest to longest if the sides are 3, 5, and 7.

Back

3, 5, 7.

Front

Identify the shortest side of a triangle with sides 6, 8, and 10.

Back

6.

Front

Identify the longest side of a triangle with sides 9, 12, and 15.

Back

15.

Front

What is the range of possible lengths for the third side of a triangle with sides 5 and 10?

Back

The third side must be greater than 5 and less than 15.

Front

If one side of a triangle is 4 and another is 7, what is the maximum length of the third side?

Back

The maximum length of the third side is less than 11.

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 a triangle has sides of lengths 8, 15, and x, what is the range of values for x?

Back

x must be greater than 7 and less than 23.

Front

What happens if the sum of two sides of a triangle is equal to the third side?

Back

The triangle is degenerate, meaning it collapses into a straight line.