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

Can the side lengths 3, 5, and 5 form a triangle?

Back

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

Front

What is the range of values for the third side (x) if two sides are 8 and 15?

Back

The range is between 7 and 23.

Front

What is the range of values for the third side (x) if two sides are 4 and 12?

Back

The range is between 8 and 16.

Front

If the longest side of a triangle is 10, what must be true about the other two sides?

Back

The sum of the lengths of the other two sides must be greater than 10.

Front

Given two sides of lengths 7 mm and 4 mm, what is the range for the third side?

Back

The range is 3 < x < 11.

Front

What happens if the sum of two sides is equal to the third side?

Back

The three points are collinear, and they do not form a triangle.

Front

What is the minimum length of the third side if the other two sides are 5 and 9?

Back

The minimum length is 5, since 5 + 5 > 9.

Front

What is the maximum length of the third side if the other two sides are 6 and 10?

Back

The maximum length is 15, since 6 + 10 > x.

Front

If one side of a triangle is 12, what is the range for the other two sides if they are both equal?

Back

The range is 0 < x < 24.