Geometric Mean and Simplifying Radicals

Front

What is the geometric mean of two numbers a and b?

Back

The geometric mean is the square root of the product of the two numbers: √(a * b).

Front

What is the SAS similarity criterion?

Back

The SAS (Side-Angle-Side) similarity criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What is the AA similarity criterion?

Back

The AA (Angle-Angle) similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the SSS similarity criterion?

Back

The SSS (Side-Side-Side) similarity criterion states that if the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

If two figures are similar, what can be said about their corresponding sides?

Back

The corresponding sides of similar figures are proportional.

Front

How do you find the geometric mean of 5 and 8?

Back

The geometric mean is √(5 * 8) = √40 = 2√10.

Front

What is the relationship between the geometric mean and the arithmetic mean?

Back

The geometric mean is always less than or equal to the arithmetic mean, except when all numbers are the same.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if they have the same shape but not necessarily the same size.

Front

What is the formula for simplifying a radical expression?

Back

To simplify a radical, factor the number under the radical into its prime factors and then take out pairs of factors as whole numbers.