Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If two sides of a triangle are 5 and 5, what is a possible length for the third side?

Back

A possible length for the third side is 9.

Front

What is the relationship between the longest side of a triangle and its angles?

Back

The largest angle of a triangle is always opposite the longest side.

Front

What is the minimum length of the third side if two sides are 2 and 6?

Back

The minimum length of the third side must be greater than 4.

Front

If the sides of a triangle are 13 and 4, what is a possible length for the third side?

Back

A possible length for the third side is 12.

Front

What is the maximum length of the third side if two sides are 2 and 6?

Back

The maximum length of the third side must be less than 8.

Front

Which angle is the smallest in a triangle with sides 5, 5, and 9?

Back

The smallest angle is ∠B, opposite the shortest side.

Front

Can a triangle be formed with sides of lengths 2, 6, and 4?

Back

No, a triangle cannot be formed because 2 + 4 is not greater than 6.

Front

What is the Triangle Inequality condition for sides a, b, and c?

Back

The conditions are: a + b > c, a + c > b, and b + c > a.

Front

If a triangle has sides of lengths 7, 10, and x, what is the range of possible values for x?

Back

x must be greater than 3 and less than 17.