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## Constructions

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**Find the perpendicular line to L1 through the external point**P. Note that the perpendicular bisector of the segment will not go through point P.**Do you understand ?**We can not use the fish on points A and B.**Let us find 2 points on the line that are equidistant from**point P. Why ? So we can go fishing. It’s a fluke ! Catfish ?**Swing a compass from**point P through the segment.**This will create a segment cd which has P on its**perpendicular bisector. This technique will be called …. The Smile technique**Now we construct the fish using points c and d.**Swing an arc from point c.**Swing an arc from point d.**Construct a line through the blue points of intersections.**Note that the procedure is just**aSmile and a Fish.**Let us try this again.**Create a perpendicular line though P. Create the smile.**Note that the segment needs to be extended.**Now, we are ready to construct the fish.**Swing arc from point c.**Swing arc from point d. Construct line through the points of arc intersections.**Review**To construct a perpendicular line from an external point to a given line, there are 2 steps. A Smile and A Fish**Construct a perpendicular line**through point P. Note that the perpendicular bisector of the segment will not go through point P.**Look**Do you think you know how to construct the perpendicular through P ? Correct ! A smile and a fish.**First the smile.**Now the fish. Construct an arc from X Construct an arc from y Construct line through the points of arc intersections.**Summary**Note that the technique for constructing a perpendicular to a line from an exterior point is the same as constructing a perpendicular to a line through a point on the line. A Smile and a Fish.**Set the compass to the distance between the arc**intersection points on**Construct // line from the intersection point**to point P From above swing an arc from top point across the bottom point.**Summary**To construct a perpendicular line through either an external or an internal point the technique is called… A Smile and a Fish.**Summary**To construct a parallel line through an external point, just construct a non-parallel line through the external point. Then duplicate an angle below to the same relative position above.**To construct a parallel line to an existing line**though an external point 1. Construct a line through both the external point and the existing line. P**To construct a parallel line to an existing line**though an external point 1. Construct a line through both the external point and the existing line. 2. Copy the new top angle to the right to point P directly above it. P**To construct a parallel line to an existing line**though an external point 1. Construct a line through both the external point and the existing line. P 2. Copy the new top angle to the right to point P directly above it. 3. Construct the // line through point P and arc intersection point. Voila !**C’est fini.**Good day and good luck. That’s all folks. A Senior Citizen Production