“geometry will be important to you later in life because there’s going to be a test six weeks...

“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