Constructions

//and lines

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

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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.