Question

If Z8, Z10, and Z11, which describes all the lines that must be parallel?

A. Only lines r and s must be parallel.
B. Only lines t and u must be parallel.
C. Lines r and s and lines t and u must be parallel.
D. Neither lines r and s nor lines t and u must be parallel.

Answer 1

If Z8, Z10, and Z11, the lines r and s and lines t and u must be parallel (option C).

Step-by-step explanation:

If Z8, Z10, and Z11, it means that angles 8, 10, and 11 are corresponding angles. Corresponding angles are formed when a transversal intersects two parallel lines. Therefore, lines r and s must be parallel, and lines t and u must be parallel.

This conclusion is based on the Corresponding Angles Postulate, which states that if a transversal intersects two parallel lines, then the pairs of corresponding angles are congruent. In this case, Z8, Z10, and Z11 are corresponding angles, indicating that lines r and s and lines t and u are parallel.

So, option C, which states that both sets of lines must be parallel, is the correct answer.

Answer 2

If Z8, Z10, and Z11, Only lines r and s must be parallel. So, the option A describes all the lines that must be parallel - only lines r and s.

Step-by-step explanation:

The given information establishes that lines Z8, Z10, and Z11 are all parallel to each other and aligned along the x-axis.

In a coordinate system, lines parallel to the x-axis maintain a consistent y-coordinate while varying in the x-coordinate.

Since all three lines share this parallelism along the x-axis, they exhibit identical slopes, indicating their equivalence in terms of direction.

Furthermore, parallel lines never intersect, reinforcing the notion that these lines share a common orientation along the x-axis without converging or diverging.

The statement "Only lines r and s must be parallel" contradicts the established parallelism of Z8, Z10, and Z11, as all three lines, including r and s, exhibit this characteristic parallelism along the x-axis.

Therefore, The option A is correct, not only lines r and s but also lines Z8, Z10, and Z11 are parallel to each other.