Constructing Perpendicular and Parallel LinesAdapted from Walch Education

Perpendicular Lines and Bisectors

• Perpendicular lines are two lines that intersect at a right angle (90˚).

• A perpendicular line can be constructed through the midpoint of a segment. This line is called the perpendicular bisector of the line segment.

• It is possible to construct a perpendicular line through a point on the given line as well as through a point not on a given line.

1.2.3: Constructing Perpendicular and Parallel Lines 2

1.2.3: Constructing Perpendicular and Parallel Lines 3

Constructing a Perpendicular Bisector of a

Line Segment Using a Compass

1. To construct a perpendicular bisector of , put the

sharp point of your compass on endpoint A. Open

the compass wider than half the distance of .

2. Make a large arc intersecting .

3. Without changing your compass setting, put the

sharp point of the compass on endpoint B. Make a

second large arc. It is important that the arcs

intersect each other.

(continued)

AB

AB

AB

4. Use your straightedge to connect the points of

intersection of the arcs.

5. Label the new line .

Do not erase any of your markings.

is perpendicular to line . AB

1.2.3: Constructing Perpendicular and Parallel Lines 4

Constructing a Perpendicular Bisector of a

Line Segment Using Patty Paper

1. Use a straightedge to construct onto patty paper.

2. Fold the patty paper so point A meets point B. Be

sure to crease the paper.

3. Unfold the patty paper.

4. Use your straightedge to mark the creased line.

5. Label the new line .

is perpendicular to line .

AB

AB

1.2.3: Constructing Perpendicular and Parallel Lines 5

Constructing a Perpendicular Line Through a Point

on the Given Line Using a Compass

1. To construct a perpendicular line through the point,

A, on a line, put the sharp point of your compass on

point A. The opening of the compass does not

matter, but try to choose a setting that isn’t so large

or so small that it’s difficult to make markings.

2. Make an arc on either side of point A on the line.

Label the points of intersection C and D.

3. Place the sharp point of the compass on point C.

Open the compass so it extends beyond point A.

(continued)

1.2.3: Constructing Perpendicular and Parallel Lines 6

4. Create an arc on either side of the line.

5. Without changing your compass setting, put the

sharp point of the compass on endpoint D. Make a

large arc on either side of the line. It is important that

the arcs intersect each other.

6. Use your straightedge to connect the points of

intersection of the arcs.

7. Label the new line .

Do not erase any of your markings.

is perpendicular to line through point A. CD

1.2.3: Constructing Perpendicular and Parallel Lines 7

Constructing a Perpendicular Line Through a Point

on the Given Line Using Patty Paper

1. Use a straightedge to construct a line, , on the patty

paper. Label a point on the line A.

2. Fold the patty paper so the line folds onto itself

through point A. Be sure to crease the paper.

3. Unfold the patty paper.

4. Use your straightedge to mark the creased line.

5. Label the new line .

Line is perpendicular to line through point A.

1.2.3: Constructing Perpendicular and Parallel Lines 8

Constructing a Perpendicular Line Through a Point

Not on the Given Line Using a Compass

1. To construct a perpendicular line through the point,

G, not on the given line , put the sharp point of your

compass on point G. Open the compass until it

extends farther than the given line.

2. Make a large arc that intersects the given line in

exactly two places. Label the points of intersection C

and D.

(continued)

1.2.3: Constructing Perpendicular and Parallel Lines 9

3. Without changing your compass setting, put the

sharp point of the compass on point C. Make a

second arc below the given line.

4. Without changing your compass setting, put the

sharp point of the compass on point D. Make a third

arc below the given line. The third arc must intersect

the second arc.

5. Label the point of intersection E.

6. Use your straightedge to connect points G and E.

Label the new line .

Do not erase any of your markings.

Line is perpendicular to line through point G.

1.2.3: Constructing Perpendicular and Parallel Lines 10

Constructing a Perpendicular Line Through a Point

Not on the Given Line Using Patty Paper

1. Use a straightedge to construct a line, , on the patty

paper. Label a point not on the line, G.

2. Fold the patty paper so the line folds onto itself

through point G. Be sure to crease the paper.

3. Unfold the patty paper.

4. Use your straightedge to mark the creased line.

5. Label the new line .

Line is perpendicular to line through point G.

Parallel Lines

• Parallel lines are lines that either do not share any points and never intersect, or share all points.

• Any two points on one parallel line are equidistant from the other line.

• There are many ways to construct parallel lines.

• One method is to construct two lines that are both perpendicular to the same given line.

1.2.3: Constructing Perpendicular and Parallel Lines 11

1.2.3: Constructing Perpendicular and Parallel Lines 12

Constructing a Parallel Line Using a Compass

1. To construct a parallel line through a point, A, not on

the given line , first construct a line perpendicular

to .

2. Put the sharp point of your compass on point A.

Open the compass until it extends farther than line

3. Make a large arc that intersects the given line in

exactly two places. Label the points of intersection

C and D.

(continued)

1.2.3: Constructing Perpendicular and Parallel Lines 13

4. Without changing your compass setting, put the

sharp point of the compass on point C. Make a

second arc below the given line.

5. Without changing your compass setting, put the

sharp point of the compass on point D. Make a third

arc below the given line. The third arc must intersect

the second arc.

6. Label the point of intersection E.

7. Use your straightedge to connect points A and E.

Label the new line . Line is perpendicular to

line .

(continued)

1.2.3: Constructing Perpendicular and Parallel Lines 14

8. Construct a second line perpendicular to line .

9. Put the sharp point of your compass on point A.

Open the compass until it extends farther than line

8. Make a large arc that intersects line in exactly

two places. Label the points of intersection F and G.

9. Without changing your compass setting, put the

sharp point of the compass on point F. Make a

second arc to the right of line .

(continued)

1.2.3: Constructing Perpendicular and Parallel Lines 15

12. Without changing your compass setting, put the

sharp point of the compass on point G. Make a third

arc to the right of line . The third arc must intersect

the second arc.

13. Label the point of intersection H.

14. Use your straightedge to connect points A and H.

Label the new line .

Do not erase any of your markings.

Line is perpendicular to line .

Line is parallel to line .

1.2.3: Constructing Perpendicular and Parallel Lines 16

Constructing a Parallel Line Using Patty Paper

1. Use a straightedge to construct line on the patty

paper. Label a point not on the line A.

2. Fold the patty paper so the line folds onto itself

through point A. Be sure to crease the paper.

3. Unfold the patty paper.

4. Fold the new line onto itself through point A.

5. Unfold the patty paper.

6. Use your straightedge to mark the second creased

line.

7. Label the new line .

Line is parallel to line .

THANKS FOR WATCHING!

Dr. Dambreville