Triangle Inequalities

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

List the conditions for forming a triangle with sides a, b, and c.

Back

1. a + b > c 2. a + c > b 3. b + c > a

Front

Can a triangle be formed with side lengths 10, 12, 22?

Back

No, because 10 + 12 is not greater than 22.

Front

Can a triangle be formed with side lengths 4, 7, 10?

Back

Yes, because 4 + 7 > 10, 4 + 10 > 7, and 7 + 10 > 4.

Front

What is the largest angle in a triangle?

Back

The largest angle is opposite the longest side.

Front

If a triangle has sides of lengths 15, 12, and 9, does it exist?

Back

Yes, because 15 + 12 > 9, 15 + 9 > 12, and 12 + 9 > 15.

Front

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

Back

In a triangle, larger angles are opposite longer sides.

Front

Can a triangle be formed with side lengths 17, 9, 30?

Back

No, because 17 + 9 is not greater than 30.

Front

What is the sum of the angles in any triangle?

Back

The sum of the angles in any triangle is always 180 degrees.

Front

If one angle of a triangle is 90 degrees, what type of triangle is it?

Back

It is a right triangle.