Question

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 so you notice about the ratios of the lengths for each transversal? How do they compare?

Answer 1

The ratio of the length of each transversal will be  $\frac{\overline {CB}}{ \overline {AB}} = \frac{\overline {EF}}{\overline{DE}} =1$

The ratio of the lines can be compared using Three Parallel Lines Theorem.

What is Three Parallel Lines Theorem?

When two transversals are intersected by three parallel lines, the transversals are proportionally divided.

According to the three parallel lines theorem, the segments created by each transversal and the three parallel lines are proportionate.

The findings are:

• The ratio of the lengths of each transversal is equal because the parallel lines divide the transversals in an equal number of halves.
•  $Ratio\ of\ segments: \frac{\overline {CB}}{ \overline {AB}} = \frac{\overline {EF}}{\overline{DE}}$

Reasons:

The question is a four part question

Let the equations of the parallel lines be as follows;

Line, x; y = x

Line, y; y = x + 1

Line z; y = x + 2

The points at which transversal 1 intersect the lines x, y, and z, are;

A(0.4, 0.4), B(0.6, 1.6), and C(0.8, 2.8)

The length of segment ${\overline {AB}}$  = √((0.6 - 0.4)² + (1.6 - 0.4)²) = 0.2·√(37)

The length of segment ${\overline {CB}}$ = √((0.8 - 0.6)² + (2.8 - 1.6)²) = 0.2·√(37)

The ratio of the lengths of the segment formed by transversal 1 is therefore;

         $\sqrt{x} \ ratio\ of\ the\ length \ of segments =\frac{\overline {CB}}{ \overline {AB}} = \frac{2.\sqrt{37} }{2.\sqrt{37} } =1$

The points at which transversal 2 intersect the lines x, y, and z, are;

D(1.1, 3.1), E(1.3, 2.3), and F(1.5, 1.5)

The length of segment  ${\overline {DE}}$= √((1.3 - 1.1)² + (2.3 - 3.1)²) = 0.2·√(17)

The length of segment ${\overline {EF}}$ = √((1.5 - 1.3)² + (1.5 - 2.3)²) = 0.2·√(17)

The ratio of the lengths of the segment formed by transversal 2 is therefore;

$\sqrt{x} \ ratio\ of\ the\ length \ of segments =\frac{\overline {EF}}{ \overline {DE}} = \frac{0.2.\sqrt{17} }{0.2.\sqrt{17} } =1$

Therefore;

            $\frac{\overline {CB}}{ \overline {AB}} = \frac{\overline {EF}}{\overline{DE}} =1$

Which gives;

• The proportion by which the transversals are divided by the parallel lines is equal.
• Each transversal's length is proportionately equal.

The the comparison can also be made with the triangle proportionality theorem.

To know more about Triangle Proportionality Theorem visit,

brainly.com/question/8160153

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