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“Geometry will be important to you later in life because there’s going to
be a test six weeks from now.”
3.8 Constructing
Parallel and
Perpendicular Lines
You will construct parallel and
perpendicular lines. You will use constructions to
explore attributes of geometric figures.
First, let’s review how to bisect an angle. Given an angle…
First, let’s review how to bisect an angle. Make an arc at the
vertex….
First, let’s review how to bisect an angle. Go to the intersection
of the arc and angleand make an arc.
First, let’s review how to bisect an angle.
Now, the other intersection and
make a arc
First, let’s review how to bisect an angle. Connect the
intersection & vertex
Now, let’s construct the line parallel to a given line and
through a given point that is not on the line.
Draw a linethrough the point
to the line.
Now, let’s construct the line parallel to a given line and
through a given point that is not on the line.
Make an arc.
Now, let’s construct the line parallel to a given line and
through a given point that is not on the line.
Make another arc.
Now, let’s construct the line parallel to a given line and
through a given point that is not on the line.
Measure the arc.
Now, let’s construct the line parallel to a given line and
through a given point that is not on the line.
Using the measure, make another arc.
Now, let’s construct the line parallel to a given line and
through a given point that is not on the line.
Connect the intersectionand the dot
Now, you try it with the line and point you were given.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Start off by drawing a point.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Measure line b
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Place the compass point on the dot you drew…
and make an arc.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Now, draw the segment.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Next draw a point not onthe line, and connect the two dots.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
With the compass point on the first dot, create an arc.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Repeat the last step with the second dot.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Position the compass point halfway between thefirst arc and the first dot,draw an arc.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Repeat the last step with the second dot;draw an arc.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Measure line a.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Place compass point onthe second dot, and draw an arc.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Connect the second arc with the second dot passing through the twointersecting arcs.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Construct a line on theright side connecting thearc with the line and thelower arc.
How about making a quadrilateral with one pair of parallel sides (a||
b).a
b
Do you see thequadrilateral?
End day 1
3.8 Constructing
Parallel and
Perpendicular Lines
(part deux)
You will construct parallel and
perpendicular lines. You will use constructions to
explore attributes of geometric figures.
One last one. Let’s make a line perpendicular to another line going through a point not on the line.
Create an arc from thepoint that cuts the
line.
One last one. Let’s make a line perpendicular to another line going through a point not on the line.
Create an arc from thepoint that cuts the
line.
From the intersectionsmake a smaller arc
that goes more than a fourth of the way around.
Repeat step 3 from the other direction.
Next, connect the point with the intersection
of the two arcs,
Bisect the angle. Draw a line parallel to the given line through the given point.
Make quadrilateral with one pair of parallel sides (a||b).
a b
Draw a line perpendicular to the given line through the given point
Perpendicular From a Point to a Line
Perpendicular From a Point to a Line
Perpendicular to a Point
Assignment
Bisect the angle. Draw a line parallel to the given line through the given point.
Make quadrilateral with one pair of parallel sides (a||b).
a b
Draw a line perpendicular to the given line through the given point
Geometry 3.8 Constructing Parallel and Perpendicular Lines3.8 Constructing Parallel and Perpendicular Lines
Bisect the angles. {3 angles} Draw a line parallel to the given line through the given point. { 2 sets}
Make quadrilateral with one pair of parallel sides (a||b).
a b
Draw a line perpendicular to the given line through the given point. { 2 sets}
Geometry 3.8 Constructing Parallel and Perpendicular Lines3.8 Constructing Parallel and Perpendicular Lines
Construct a rectangle with base a and height b. Construct a square with side of length a.
a b
Geometry 3.8 Constructing Parallel and Perpendicular Lines3.8 Constructing Parallel and Perpendicular Lines
a
