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 sides 4, 7, and 8 form a triangle?

Back

Yes, because 4 + 7 > 8, 4 + 8 > 7, and 7 + 8 > 4.

Front

Can the sides 7, 5, and 4 form a triangle?

Back

Yes, because 7 + 5 > 4, 7 + 4 > 5, and 5 + 4 > 7.

Front

Can the sides 3, 10, and 8 form a triangle?

Back

Yes, because 3 + 10 > 8, 3 + 8 > 10, and 10 + 8 > 3.

Front

Can the sides 3, 6, and 2 form a triangle?

Back

No, because 3 + 2 is not greater than 6.

Front

Can the sides 2, 15, and 16 form a triangle?

Back

Yes, because 2 + 15 > 16, 2 + 16 > 15, and 15 + 16 > 2.

Front

What is the first condition of the Triangle Inequality Theorem?

Back

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

Front

What is an example of a set of numbers that cannot form a triangle?

Back

The numbers 1, 2, and 3 cannot form a triangle because 1 + 2 is not greater than 3.

Front

If a triangle has sides of lengths 5, 5, and 10, can it exist?

Back

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

Front

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

Back

It helps determine whether three given lengths can form a triangle.