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 6, 6, and 3 form a triangle?

Back

Yes, because 6 + 6 > 3, 6 + 3 > 6, and 6 + 3 > 6.

Front

Can the sides 8, 10, and 20 form a triangle?

Back

No, because 8 + 10 is not greater than 20.

Front

Can the sides 6, 5, and 8 form a triangle?

Back

Yes, because 6 + 5 > 8, 6 + 8 > 5, and 5 + 8 > 6.

Front

Can the sides 6, 10, and 8 form a triangle?

Back

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

Front

Can the sides 9, 12, and 22 form a triangle?

Back

No, because 9 + 12 is not greater than 22.

Front

What is the condition for three lengths to form a triangle?

Back

The lengths a, b, and c must satisfy: a + b > c, a + c > b, and b + c > a.

Front

If a triangle has sides of lengths 7, 10, and 5, can it exist?

Back

Yes, because 7 + 5 > 10, 7 + 10 > 5, and 10 + 5 > 7.

Front

If a triangle has sides of lengths 3, 4, and 8, can it exist?

Back

No, because 3 + 4 is not greater than 8.

Front

What happens if the sum of two sides equals the third side?

Back

The three lengths will form a degenerate triangle, which is a straight line.