Inequalities in One Triangle (Section 5-3)

Front

What is the Transitive Property of Inequality?

Back

If a > b and b > c, then a > c.

Front

What is the Definition of Inequality?

Back

For any real numbers a and b, a > b if there exists a positive number c such that a = b + c.

Front

List the angles in a triangle from greatest to least based on their opposite sides.

Back

The angle opposite the longest side is the greatest, and the angle opposite the shortest side is the least.

Front

What is the Comparison Property of Inequality?

Back

For any real number x, x < 0, x = 0, or x > 0.

Front

What is the Subtraction Property of Inequality?

Back

If a > b, then a - c > b - c for any real number c.

Front

What is the Multiplication Property of Inequality?

Back

If a > b and c > 0, then ac > bc.

Front

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

Back

The larger the angle, the longer the opposite side.

Front

If two sides of a triangle are equal, what can be said about the angles opposite those sides?

Back

The angles opposite the equal sides are also equal.

Front

How do you determine the shortest side of a triangle?

Back

The shortest side is opposite the smallest angle.

Front

What is the Triangle Inequality Theorem?

Back

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