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 side lengths 7 yd, 8 yd, and 9 yd form a triangle?

Back

Yes, because 7 + 8 > 9, 7 + 9 > 8, and 8 + 9 > 7.

Front

Can the side lengths 3, 5, and 8 form a triangle?

Back

No, because 3 + 5 is not greater than 8.

Front

What is the condition for three sides 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 15 in., 12 in., and 2 in., can they form a triangle?

Back

No, because 15 + 2 is not greater than 12.

Front

What does it mean if three angles measure 55°, 45°, and 90°?

Back

No triangle exists because the sum of the angles exceeds 180°.

Front

What is the maximum angle measure in a triangle?

Back

The maximum angle measure in a triangle is less than 180°.

Front

What is the minimum side length required to form a triangle with sides of lengths 5 and 7?

Back

The minimum side length must be greater than 2 (5 - 7 < x < 5 + 7).

Front

What is an example of side lengths that cannot form a triangle?

Back

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

Front

What is the relationship between the angles and sides of a triangle?

Back

In a triangle, the larger the angle, the longer the opposite side.