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;
[tex]\displaystyle \frac{AB}{CB} = \mathbf{\frac{0.1 \cdot \sqrt{37} }{0.1 \cdot \sqrt{37}}} = 1[/tex]
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;
[tex]\displaystyle \frac{EF}{DE} =\frac{0.1 \cdot \sqrt{17} }{0.1 \cdot \sqrt{17}} = 1[/tex]
Therefore:
The ratio of the lengths of the two line segments formed on each transversal are equal.
Learn more about parallel lines here:
https://brainly.com/question/11495328
