Constructions // and lines
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Find the perpendicular line to L1 through the external point P.
BA
P
Note that the perpendicular bisector of the segment will not go through point P.
BA
P
Do you understand ?
We can not use the fish on points A and B.
BA
P 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 ?
dc
BA
P
Swing a compass from point P through the segment.
BA
P
dc
BA
P
This will create a segment cd which has P on its perpendicular bisector.
This technique will be called ….
The Smile technique
dc
BA
P Now we construct the fish using points c and d.
Swing an arc from point c.
dc
BA
P Swing an arc from point d.
Construct a line through the blue points of intersections.
dc
BA
P
Note that the procedure is just
a Smile and a Fish.
Let us try this again.
BA
PCreate the smile.
Create a perpendicular line though P.
BA
PNote that the segment needs to be extended.
dc
BA
P
Now, we are ready to construct the fish.
dc
BA
PSwing arc from point c.
dc
BA
P Swing arc from point d.
Construct line through the points of arc intersections.
ReviewTo construct a perpendicular line from an external point to a given line, there are 2 steps.
A Smileand
A Fish
BA
P
Note that the perpendicular bisector of the segment will not go through point P.
Construct a perpendicular line through point P.
BA
P
Do you think you know how to construct the perpendicular through P ?
Correct ! A smile and a fish.
Look
yx BA
P First the smile.
Now the fish.Construct an arc from X
yx BA
P
yx BA
PConstruct line through the points of
arc intersections.
Construct an arc from y
SummaryNote 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.
Constructing
a // line thru a Pt.
P
BA
P
BA
Construct a line through P which intersects AB
U
P
BA
. .Copy PUB to pt P
U
P
BA.Swing arc across PUB
Duplicate the arc at point P.
U
P
BASet the compass to the distance
between the arc intersection points on PUB
U
P
BA
Swing an arc from bottom point across the top point.
U
P
BA
From above swing an arc from top point across the bottom point.
Construct // line from the intersection point to point P
SummaryTo construct a perpendicular line through either an external or an internal point the technique is called…
A Smile
and a Fish.dc
BA
P
SummaryTo 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.
U
P
BA
To construct a parallel line to an existing linethough 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 linethough 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 linethough 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
3. Construct the // line through point P and arc intersection point.
Voila !
C’est fini.Good day and good luck.
A Senior Citizen Production
That’s all folks.
Related Documents
