Question

We are given that lines a and c intersect at point S. Translate line a down line c until point S reaches point Q. Call the new line through Q line b. Because translations preserve orientation, lines a and b are ________. Because translations preserve angle measure, ∠RSU ≅ ∠RQU'. For the same reason, ∠RST ≅ ∠RQT', ∠PSU ≅ ∠PQU', and ∠PST ≅ ∠PQT'. Each of the angle pairs are corresponding angles. Therefore, corresponding angles are congruent

Answer 1

parallel

Explanation:

Knowing that translations preserve orientation, then the angle formed in the intersection of lines a and c, and in the intersection of lines b and c are the same. If two different lines form the same angle when intercepting a third different line, then they are parallel.

Answer 2

The lines a and b are parallel

Explanation:

When we will translate line a, then the new line b will be formed.

Now, as translation preserves orientation each point on line a will be equidistant from line b , thus holding the condition and satisfying the property of two parallel lines.

Hence, line a and line b are parallel to each other.