Question

ab and pq are parallel lines. (overleftrightarrow{cr}) and (overleftrightarrow{ds}) intersect the two lines as shown in the figure. which statement is true about cr and ds?

a. (cr < ds)

b. (cr > ds)

c. (cr = ds)

d. (cr = ds \times 2)

Explanation:

In the given figure, \( \overleftrightarrow{AB} \) and \( \overleftrightarrow{PQ} \) are parallel lines. \( \overline{CR} \) and \( \overline{DS} \) are both perpendicular to these parallel lines (as indicated by the right angles at \( C \) and \( D \)). The distance between two parallel lines is constant, and segments perpendicular to both parallel lines (like \( \overline{CR} \) and \( \overline{DS} \)) are equal in length because they represent the distance between the parallel lines. So, \( CR = DS \).

Answer:

C. \( CR = DS \)