Exploring Adding and Subtracting Rational Expressions

What theorem is used to establish the similarity of right triangles when an altitude is drawn to the hypotenuse?

• Right Triangle Similarity Theorem

• Pythagorean Theorem

• Triangle Inequality Theorem

• Angle-Side-Angle Postulate

In the context of similar triangles, what does it mean for sides to be corresponding?

• They are parallel to each other

• They are opposite to equal angles

• They are of equal length

• They maintain the same proportion across triangles

What is the relationship between the sides of similar triangles?

• They are congruent

• They are parallel

• They are proportional

• They are perpendicular

How do you determine the geometric mean of two numbers, a and b?

• sqrt(a * b)

• a * b

• a + b / 2

• (a + b) / 2

What is the geometric mean in the context of a right triangle with an altitude?

• The square root of the product of the segments created by the altitude

• The length of the hypotenuse

• The length of the altitude

• The product of the segments created by the altitude

If the altitude of a right triangle divides the hypotenuse into segments of lengths 8 and 12, what is the length of the altitude?

• 2 sqrt(30)

• 4 sqrt(6)

• sqrt(96)

• 10

In a right triangle, if one leg squared equals the product of the hypotenuse and the segment of the hypotenuse adjacent to the leg, what does this describe?

• Triangle Proportionality Theorem

• Similar Triangles Property

• Geometric Mean Theorem

• Pythagorean Theorem

What is the geometric mean of the numbers 16 and 28?

• 6 sqrt(5)

• 4 sqrt(14)

• 8 sqrt(7)

• 12 sqrt(3)

How is the geometric mean used to find the length of an altitude in a triangle?

• By dividing the hypotenuse by the altitude

• By multiplying the lengths of the two segments created by the altitude

• By taking the square root of the product of the segments' lengths

• By adding the segments' lengths and dividing by two

If the altitude is 21 and it divides the hypotenuse into segments of 30 and x, what is the value of x if the altitude squared equals the product of the segments?

• 44.7

• 30

• 15.5

• 14.7