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

Will the sides 5 cm, 7 cm, and 10 cm form a triangle?

Back

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

Front

Will the sides 15 in., 12 in., and 2 in. form a triangle?

Back

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

Front

What is the total sum of angles in a triangle?

Back

180 degrees.

Front

Which of the following sets of lengths can form a triangle: (2 cm, 6 cm, 7 cm) or (2 cm, 5 cm, 8 cm)?

Back

(2 cm, 6 cm, 7 cm) can form a triangle, but (2 cm, 5 cm, 8 cm) cannot.

Front

If a = 3 and b = 4, what is the length of c in a right triangle?

Back

c = 5, using the Pythagorean theorem.

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

Can a triangle have sides of lengths 1 cm, 2 cm, and 3 cm?

Back

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

Front

What is an example of a set of lengths that can form a triangle?

Back

3 cm, 4 cm, and 5 cm.

Front

What is the relationship between the sides of a triangle?

Back

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