Calculate the ratio of the lengths of the two line segments formed on each transversal. You will have two sets of calculations. Round your answers to the hundredths place. What do you notice about the ratios of the lengths for each transversal? How do they compare?

The relationship between the line segments formed on each transversal is

given by the three parallel lines theorem.

Reasons:

The question is a four part question, with part A being to construct three parallel lines and two transversals to intersect the parallel lines

The equation of the parallel lines are;

y = x, and y = x + 1

The point of intersection of transversal 1 and the parallel lines y, and z

(0.2, 0.2), and (0.3, 0.8)

The length of segment AB = √((0.3 - 0.2)² + (0.8 - 0.2)²) = 0.1·√(37)

The point of intersection of transversal 1 and the parallel lines x, and y

(0.3, 0.8), and (0.4, 1.4)

The length of segment CB = √((0.4 - 0.3)² + (1.4 - 0.8)²) = 0.1·√(37)

The ratio of the lengths of the line segments formed by the transversal 1, AB:CB is found as  follows;

The point of intersection of transversal 2 and the parallel lines y and z are;

(0.8, 0.8), and (0.7, 1.2)

The length of segment EF = √((0.7 - 0.8)² + (1.2 - 0.8)²) = 0.1·√(17)

The point of intersection of transversal 2 and the parallel lines x and y are;

(0.7, 1.2), and (0.6, 1.6)

The length of segment DE = √((0.6 - 0.7)² + (1.6 - 1.2)²) = 0.1·√17

The ratio of the lengths of the line segments formed by the transversal 2, EF:DE is found as  follows;

Therefore:

The ratio of the lengths of the two line segments formed on each transversal are equal.

Learn more about parallel lines here:

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answer: 2530

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the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: