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

If the sides of a triangle are 3, 4, and 5, do they satisfy the Triangle Inequality Theorem?

Back

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

Front

Can the side lengths 2, 2, and 4 form a triangle?

Back

No, because 2 + 2 is not greater than 4.

Front

What is the minimum requirement for three lengths to form a triangle?

Back

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

Front

If the side lengths are 7, 7, and 7, do they form a triangle?

Back

Yes, because 7 + 7 > 7.

Front

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

Back

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

Front

For the side lengths 5, 10, and 15, do they form a triangle?

Back

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

Front

What is an example of side lengths that do form a triangle?

Back

Side lengths 6, 8, and 10 form a triangle because 6 + 8 > 10.

Front

If a triangle has sides of lengths 1, 2, and 3, can it exist?

Back

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

Front

What is the significance of the Triangle Inequality Theorem in geometry?

Back

It helps determine whether a set of lengths can form a triangle.