Geometry - Flashcard 5.2

Front

What is the definition of similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

How do you find the missing side length in similar triangles?

Back

Use the ratio of the lengths of corresponding sides of the triangles to set up a proportion and solve for the missing length.

Front

What is the geometric mean of two numbers?

Back

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

Front

What is the formula for the altitude to the hypotenuse in a right triangle?

Back

If AD and DB are segments of the hypotenuse, then the length of the altitude CD can be found using the formula: CD = √(AD * DB).

Front

What is the similarity statement for triangles?

Back

A statement that indicates two triangles are similar, often written as ΔABC ∼ ΔDEF, meaning triangle ABC is similar to triangle DEF.

Front

How do you calculate the geometric mean of 4 and 9?

Back

The geometric mean is √(4*9) = √36 = 6.

Front

What is the relationship between the sides of similar triangles?

Back

The ratios of the lengths of corresponding sides of similar triangles are equal.

Front

What is the significance of the altitude in a right triangle?

Back

The altitude to the hypotenuse creates two smaller right triangles that are similar to the original triangle and to each other.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if they have two corresponding angles equal or if the sides are in proportion.

Front

What is the formula for finding the geometric mean of 2 and 25?

Back

The geometric mean is √(2*25) = √50 = 5√2.