Triangle Inequality Theorem (side lengths)

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 lengths 6, 5, and 8 be the sides of a triangle?

Back

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

Front

What must be true 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

Can the lengths 8, 3, and 8 be the sides of a triangle?

Back

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

Front

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

Back

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

Front

Can the lengths 9, 3, and 10 be the sides of a triangle?

Back

Yes, because 9 + 3 > 10, 9 + 10 > 3, and 3 + 10 > 9.

Front

What is the condition for two sides of a triangle compared to the third side?

Back

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

Front

If a triangle has sides of lengths 5, 7, and 12, can it exist?

Back

No, because 5 + 7 is not greater than 12.

Front

What is an example of a valid triangle side length set?

Back

Lengths 4, 5, and 6 can form a triangle because 4 + 5 > 6, 4 + 6 > 5, and 5 + 6 > 4.

Front

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

Back

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