Triangle Inequality Practice

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 three lengths, how can you determine if they can form a triangle?

Back

To determine if three lengths can form a triangle, check if the sum of the lengths of any two sides is greater than the length of the third side for all three combinations.

Front

If the side lengths of a triangle are 6, 6, and 7, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 6 + 6 > 7, 6 + 7 > 6, and 6 + 7 > 6.

Front

Can a triangle have side lengths of 4, 11, and 13?

Back

Yes, because 4 + 11 > 13, 4 + 13 > 11, and 11 + 13 > 4.

Front

What is the shortest side of a triangle with side lengths 15, 12, and 9?

Back

The shortest side is 9.

Front

Does a triangle with side lengths 20, 10, and 9 exist?

Back

No, because 20 is not less than the sum of 10 and 9 (20 < 10 + 9).

Front

What is the significance of the longest side in a triangle?

Back

The longest side must be less than the sum of the other two sides to satisfy the Triangle Inequality Theorem.

Front

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

Back

It is an isosceles triangle.

Front

What is an equilateral triangle?

Back

An equilateral triangle is a triangle in which all three sides are of equal length.

Front

How do you identify the longest side of a triangle?

Back

The longest side is the one with the greatest numerical value among the three side lengths.