Question

How many lines can be drawn through P parallel to $\overleftrightarrow{QR}$?

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 P and the another line is $\overleftrightarrow{QR}$. Consider that the line on which P is positioned is $\overleftrightarrow{QPR}$that is having a parallel relation with $\overleftrightarrow{QR}$along with this the consideration of another line $\overleftrightarrow{APB}$will result in formation of an angle that is from the intersection between the lines $\overleftrightarrow{APB}$and $\overleftrightarrow{QPR}$.

As the lines $\overleftrightarrow{APB}$and $\overleftrightarrow{QPR}$are having an intersection so the line $\overleftrightarrow{APB}$cannot be parallel to the line $\overleftrightarrow{QR}$.

Step 3. Make the conclusion

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