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

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 range of possible lengths for the third side of a triangle with sides of lengths 4 and 12?

Back

The length of the third side must be greater than 8 and less than 16.

Front

How many degrees are in a triangle?

Back

A triangle has a total of 180 degrees.

Front

What is the shortest side in a triangle with sides QP, QM, and MP if QM is the shortest?

Back

QM is the shortest side.

Front

List the angles in order from smallest to largest if ∠A < ∠C < ∠B.

Back

∠A, ∠C, ∠B.

Front

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

Back

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

Front

If one side of a triangle is 5 and another is 7, what is the maximum length of the third side?

Back

The maximum length of the third side is less than 12.

Front

If a triangle has sides of lengths 3, 4, and x, what is the range of x?

Back

x must be greater than 1 and less than 7.

Front

What does it mean for a triangle to be degenerate?

Back

A degenerate triangle has its three points collinear, meaning the sum of the lengths of two sides equals the length of the third side.