Geometric Mean and Triangle Ratios Quiz

Why is it important to redraw triangles when solving geometric problems?

• To avoid using formulas

• To change the dimensions of the triangles

• To identify similar triangles and corresponding sides

• To make the problem look more complex

What happens when you draw an altitude in a right triangle?

• It eliminates the hypotenuse

• It changes the angles of the triangle

• It creates two more triangles

• It makes the triangle larger

Which of the following is true about the triangles created by drawing an altitude in a right triangle?

• They are not similar to the original triangle

• They have different angles than the original triangle

• They are larger than the original triangle

• They are similar to each other and the original triangle

What is the geometric mean used for in the context of triangles?

• To find the area of the triangle

• To find the angles of the triangle

• To find the altitude of the triangle

• To find the perimeter of the triangle

How do you find the altitude of a triangle using the geometric mean?

• By multiplying the lengths of the two sides and taking the square root

• By dividing the lengths of the two sides

• By subtracting the lengths of the two sides

• By adding the lengths of the two sides

What is the value of x if the sides of the triangle are 15 and 4?

• 4

• Square root of 15

• Square root of 60

• 2

What is the first step in setting up ratios to solve for side 'y'?

• Divide the sides

• Multiply the sides

• Identify the corresponding sides

• Identify the hypotenuse

What is the geometric mean of 15 and 19?

• Square root of 19

• Square root of 285

• Square root of 34

• Square root of 150

Why might you leave the value of y as the square root of 285?

• Because it is a smaller number

• Because it simplifies the problem

• Because 285 is not a perfect square

• Because it is easier to remember

What is the hypotenuse of the triangle when solving for side 'z'?

• 285

• 4

• 15

• 19