Question

Calculate the ratio of the lengths of the two line segments formed on each transversal. What do you notice about the ratios of the lengths for each transversal? How do they compare?

a) The ratio is 1:2, and it is consistent for all transversals.
b) The ratio varies for each transversal.
c) The ratio is 2:1, and it is consistent for all transversals.
d) The ratio is 3:4, and it is consistent for all transversals.

Answer 1

a) The ratio is 1:2, and it is consistent for all transversals.

Step-by-step explanation:

The consistent ratio of 1:2 for all transversals suggests parallel lines. When a transversal intersects two parallel lines, the corresponding angles are congruent, resulting in proportional segments.

This phenomenon is defined by the properties of parallel lines and transversals, indicating a consistent ratio regardless of the specific transversal chosen.

Therefore, observing a constant ratio across various transversals indicates a parallel line relationship with a consistent scale factor between corresponding line segments.