Question

How many lines can be drawn through Q parallel to $\overleftrightarrow{PR}$?

Short answer

The required count of line is one.

Step-by-step solution

Step 1. Define the theorem that can be used

Theorem 3-8 can be used which states that a parallel line to another line consist of a point that is positioned on outer area of another line.

Step 2. Relate the theorem using the provided information

The mentioned point in theorem according to the question is Q and the another line is $\overleftrightarrow{PR}$. Consider that the line on which Q is positioned is $\overleftrightarrow{PQR}$that is having a parallel relation with $\overleftrightarrow{PR}$along with this the consideration of another line $\overleftrightarrow{AQB}$will result in formation of an angle that is from the intersection between the lines $\overleftrightarrow{AQB}$and $\overleftrightarrow{PR}$.

As the lines $\overleftrightarrow{AQB}$and $\overleftrightarrow{PQR}$are having an intersection so the line $\overleftrightarrow{AQB}$cannot be parallel to the line $\overleftrightarrow{PR}$.

Step 3. Make the conclusion

As the count of line parallel to $\overleftrightarrow{PR}$is only one which results in that the required count is one.