11/13 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

Given side lengths 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

If two sides of a triangle are 7 ft and 13 ft, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 6 ft and less than 20 ft.

Front

Can the side lengths 9, 9, and 9 form a triangle?

Back

Yes, because the sum of any two sides is greater than the third side.

Front

If side AB is 10 inches and side BC is 17 inches, what could be the length of side AC?

Back

The length of side AC must be greater than 7 inches and less than 27 inches, so 16 inches is a valid length.

Front

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

Back

The segments will not form a triangle; they will be collinear.

Front

What is the minimum length of the third side if the other two sides are 8 and 5?

Back

The minimum length of the third side must be greater than 3 (8 - 5).

Front

What is the maximum length of the third side if the other two sides are 8 and 5?

Back

The maximum length of the third side must be less than 13 (8 + 5).

Front

If a triangle has sides of lengths 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

What happens if the lengths of the sides do not satisfy the Triangle Inequality Theorem?

Back

The lengths cannot form a triangle.