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

If side lengths are a, b, and c, what must be true for them to form a triangle?

Back

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

Front

Given sides of lengths 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.

Front

Can the sides 3, 6, and 12 form a triangle?

Back

No, because 3 + 6 is not greater than 12.

Front

What is the shortest side in a triangle with sides 5, 12, and 13?

Back

The shortest side is 5.

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.

Front

What is the maximum length of a side in a triangle with sides 8 and 15?

Back

The maximum length of the third side can be 22 (8 + 15 - 1).

Front

Can the lengths 7, 7, and 14 form a triangle?

Back

No, because 7 + 7 is not greater than 14.

Front

What is the relationship between the sides of a triangle and its perimeter?

Back

The perimeter of a triangle is the sum of the lengths of all three sides.

Front

If a triangle has sides of lengths 9, 9, and 9, what type of triangle is it?

Back

It is an equilateral triangle.