Question

In the plane P, Q, and R, how many lines can be drawn through R perpendicular to $\overleftrightarrow{QR}$? What postulate or theorem justifies your answer?

Short answer

The required count of line is one and the theorem is Theorem 3-9.

Step-by-step solution

Step 1. Define the theorem that can be used

Theorem 3-9 can be used which states that a perpendicular 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 R and the another line is $\overleftrightarrow{QR}$. According to the figure the line on which R is positioned is that is having a perpendicular relation with $\overleftrightarrow{QR}$along with this the consideration of another line $\overleftrightarrow{RB}$will result in formation of an angle which is not equal to localid="1637909895808" $90°$the line $\overleftrightarrow{RB}$cannot have a perpendicular relation with the line $\overleftrightarrow{QR}$.

Step 3. Make the conclusion

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