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 three sides of lengths 3, 4, and 5 form a triangle?

Back

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

Front

Can three sides of lengths 2, 2, and 5 form a triangle?

Back

No, because 2 + 2 is not greater than 5.

Front

What are the conditions for three lengths to form a triangle?

Back

The sum of any two sides must be greater than the third side.

Front

If the sides of a triangle are 6, 8, and 10, do they satisfy the Triangle Inequality Theorem?

Back

Yes, because 6 + 8 > 10, 6 + 10 > 8, and 8 + 10 > 6.

Front

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

Back

The three lengths will form a straight line, not a triangle.

Front

Can the sides of a triangle have lengths 1, 2, and 3?

Back

No, because 1 + 2 is not greater than 3.

Front

What is an example of three lengths that can form a triangle?

Back

Lengths 5, 7, and 9 can form a triangle because 5 + 7 > 9.

Front

If a triangle has sides of lengths 10, 10, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 10 + 10 > 5, 10 + 5 > 10, and 10 + 5 > 10.

Front

What is the minimum length of a side in a triangle if the other two sides are 3 and 4?

Back

The minimum length must be greater than 1 (3 - 4 < x < 3 + 4).