Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If a triangle has sides of lengths a, b, and c, what must be true?

Back

a + b > c, a + c > b, and b + c > a.

Front

What is the shortest side in a triangle?

Back

The shortest side is the one opposite the smallest angle.

Front

If the longest side of a triangle is 10, what can be said about the other two sides?

Back

The sum of the lengths of the other two sides must be greater than 10.

Front

Given side lengths of 12 cm and 14 cm, what could be the length of the third side?

Back

The third side must be greater than |12 - 14| = 2 cm and less than 12 + 14 = 26 cm.

Front

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

Back

The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

How do you determine the possible lengths of a triangle's sides?

Back

Use the Triangle Inequality Theorem: For any triangle with sides a, b, and c, the following must hold: a + b > c, a + c > b, b + c > a.

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 measures 90 degrees, what type of triangle is it?

Back

It is a right triangle.

Front

How do you list angles in order from smallest to largest?

Back

Compare the measures of the angles and arrange them accordingly.