Chapter 10.3, Problem 4ST1

To determine

To construct: the line $\overline{PQ}$ parallel to line t.

Explanation of Solution

Given information:

The given information is:

Draw any line t and choose any point not on the line t.

Procedure to construct the line $\overline{PQ}$ parallel to line t:

• Draw any line t and represent any point not on the line t.
• Indicate two points A and B on line t and draw the line $\overline{AP}$ .
• With A as a centre and any radius intersect the lines t and$\overline{AP}$, Label the point of intersections X and Y.
• With same radius intersect the lines $\overline{AP}$, Label the point of as Z.
• Measure the arc length $XY.$
• With Z as a centre and radius of $XY.$ intersect the arc drawn using P as centre. Label the point as Q.
• Join the line $PQ$

The line $\overline{PQ}$ parallel to line t is shown below.

  

Hence, the line $\overline{PQ}$ parallel to line t is shown below.