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Chapter 3: Q17 (page 86)

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

Short Answer

Expert verified

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

Step by step solution

01

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.

02

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 QR↔. According to the figure the line on which R is positioned is that is having a perpendicular relation with QR↔along with this the consideration of another line RB↔will result in formation of an angle which is not equal to localid="1637909895808" 90°the line RB↔cannot have a perpendicular relation with the line QR↔.

03

Step 3. Make the conclusion

As the count of line perpendicular to QR↔is only one which results in that the required count is one.

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