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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.”

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3.8 Constructing Parallel and Perpendicular Lines You will construct parallel and perpendicular lines. You will use constructions to explore attributes of geometric figures.

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**First, let’s review how to bisect an angle.**

Given an angle…

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**First, let’s review how to bisect an angle.**

Make an arc at the vertex….

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**First, let’s review how to bisect an angle.**

Go to the intersection of the arc and angle and make an arc.

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**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.

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**First, let’s review how to bisect an angle.**

Connect the intersection & vertex

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Now, let’s construct the line parallel to a given line and through a given point that is not on the line. Draw a line through the point to the line.

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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.

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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.

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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.

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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.

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**Connect the intersection**

Now, let’s construct the line parallel to a given line and through a given point that is not on the line. Connect the intersection and the dot

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**Now, you try it with the line and point you were given.**

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Start off by drawing a point. How about making a quadrilateral with one pair of parallel sides (a||b). a b

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Measure line b How about making a quadrilateral with one pair of parallel sides (a||b). a b

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**Place the compass point**

on the dot you drew… How about making a quadrilateral with one pair of parallel sides (a||b). and make an arc. a b

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**How about making a quadrilateral with one pair of parallel sides (a||b).**

Now, draw the segment. a b

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Next draw a point not on the line, How about making a quadrilateral with one pair of parallel sides (a||b). and connect the two dots. a b

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**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

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Repeat the last step with the second dot. How about making a quadrilateral with one pair of parallel sides (a||b). a b

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Position the compass point halfway between the first arc and the first dot, How about making a quadrilateral with one pair of parallel sides (a||b). draw an arc. a b

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**Repeat the last step with**

the second dot; How about making a quadrilateral with one pair of parallel sides (a||b). draw an arc. a b

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Measure line a. How about making a quadrilateral with one pair of parallel sides (a||b). a b

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Place compass point on the second dot, How about making a quadrilateral with one pair of parallel sides (a||b). and draw an arc. a b

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**How about making a quadrilateral with one pair of parallel sides (a||b).**

Connect the second arc with the second dot passing through the two intersecting arcs. a b

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**How about making a quadrilateral with one pair of parallel sides (a||b).**

Construct a line on the right side connecting the arc with the line and the lower arc. a b

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**How about making a quadrilateral with one pair of parallel sides (a||b).**

Do you see the quadrilateral? a b End day 1

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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.

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**One last one. Let’s make a line perpendicular to another line going through a point not on the line.**

Create an arc from the point that cuts the line.

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**One last one. Let’s make a line perpendicular to another line going through a point not on the line.**

Create an arc from the point that cuts the line.

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**From the intersections make a smaller arc that goes more than **

a fourth of the way around.

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**from the other direction.**

Repeat step 3 from the other direction.

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Next, connect the point with the intersection of the two arcs,

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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). Draw a line perpendicular to the given line through the given point a b

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**Perpendicular From a Point to a Line**

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**Perpendicular From a Point to a Line**

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**Perpendicular to a Point**

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Assignment

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**3.8 Constructing Parallel and Perpendicular Lines**

Geometry 3.8 Constructing Parallel and Perpendicular Lines 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). Draw a line perpendicular to the given line through the given point a b

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**3.8 Constructing Parallel and Perpendicular Lines**

Geometry 3.8 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). Draw a line perpendicular to the given line through the given point. { 2 sets} a b

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**3.8 Constructing Parallel and Perpendicular Lines**

Geometry 3.8 Constructing Parallel and Perpendicular Lines Construct a rectangle with base a and height b. Construct a square with side of length a. a a b

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