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

Given sides a, b, and c, what must be true for them to form a triangle?

Back

a + b > c, a + c > b, and b + c > a must all be true.

Front

Which set of side lengths can form a triangle? 3, 6, 12 or 7, 7, 14 or 9, 9, 9 or 13, 6, 7?

Back

9, 9, 9 can form a triangle.

Front

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

Back

The third side must be more than 6 ft but less than 20 ft.

Front

Can the lengths 5, 10, and 15 form a triangle?

Back

No, because 5 + 10 is not greater than 15.

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the length of AC?

Back

AC could be 16 inches.

Front

What is the longest side in a triangle?

Back

The longest side is opposite the largest angle.

Front

If the sides of a triangle are 8, 15, and x, what is the range of x?

Back

x must be more than 7 and less than 23.

Front

What happens if the sum of two sides equals the third side?

Back

The segments will be collinear and will not form a triangle.

Front

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

Back

The largest angle is opposite the longest side.