Using triangle proportionality theorem to prove parallel lines

The video tutorial covers the triangle proportionality theorem, reviewing previous class notes and explaining how to set up and calculate proportions to prove line equality. The instructor demonstrates using given values and cross multiplication to find the necessary values, concluding that for certain values, lines are parallel.

What does the triangle proportionality theorem state about the segments of a triangle with parallel lines?

• The segments are perpendicular to each other.

• The segments form a right angle.

• The ratio of two segments is equal to the ratio of two other segments.

• The segments are equal in length.

In the given problem, if the full length is 27 and one segment is 9, what is the length of the other segment?

• 18

• 36

• 9

• 27

What is the purpose of setting up a proportion in the problem-solving process?

• To calculate the perimeter of the triangle.

• To prove the equality of the lines.

• To determine the length of the hypotenuse.

• To find the area of the triangle.

How is cross-multiplication used in solving the proportion?

• By multiplying the numerators together.

• By adding the numerators and denominators.

• By multiplying the numerator of one fraction by the denominator of the other.

• By dividing the denominators by the numerators.

What is the final value of X that proves the lines are parallel?

• 1/2

• 1

• 3/4

• 2/3