Triangle Inequality Theorem and Inequalities in Triangles

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 8 cm and 5 cm, what is the range of possible lengths for the third side?

Back

3 cm < x < 13 cm.

Front

Identify the longest side in a triangle with sides 7 cm, 10 cm, and 5 cm.

Back

10 cm is the longest side.

Front

What is the minimum length of the third side if two sides of a triangle are 9 cm and 4 cm?

Back

The minimum length of the third side must be greater than 5 cm.

Front

If a triangle has sides of lengths 6 cm, 8 cm, and x cm, what must be true about x?

Back

x must satisfy 2 cm < x < 14 cm.

Front

What is the maximum length of the third side if two sides of a triangle are 15 m and 10 m?

Back

The maximum length of the third side is less than 25 m.

Front

In a triangle with sides 3 cm, 4 cm, and x cm, what is the range for x?

Back

x must be greater than 1 cm and less than 7 cm.

Front

What does it mean for a triangle to be valid?

Back

A triangle is valid if the lengths of its sides satisfy the Triangle Inequality Theorem.

Front

If one side of a triangle is 12 inches and another is 7 inches, what is the range for the third side?

Back

The range for the third side is 5 inches < x < 19 inches.

Front

Identify the shortest side in a triangle with sides 9 m, 12 m, and 15 m.

Back

9 m is the shortest side.