Constructions: Parallel Lines

Objectives:

1. To construct parallel lines with a compass

and a straightedge using the equidistant

method and the Corresponding Angles

Postulate

Definition

Parallel lines are lines that lie in the same plane and do not intersect.

If two lines in a plane are parallel, then they must always be the same distance apart. The converse of this is also true. This gives you a way, called the equidistant method, of constructing parallel lines.

Parallel Lines 1

1. Draw a line m

and a point P not

on m.

Parallel Lines 1

2. Draw a line

perpendicular to

line m through

point P. Label

the point of

intersection Q. (This was a

construction from the

previous presentation)

Parallel Lines 1

3. Draw a point R

on the line to the

right of Q.

Construct a line

n through point R

that is

perpendicular to

line m. (This was also

a construction from the

previous presentation)

Parallel Lines 1

4. Construct point

S on line n by

copying segment

QP onto line n,

with Q

corresponding to

R and P

corresponding to

S.

Parallel Lines 1

5. Draw a line

through P and S.

Parallel Lines 2

Now we’ll construct two parallel lines using a

different method. This construction relies upon

the Converse of the Corresponding Angles

Postulate; that is,

if our corresponding

angles are

congruent, then

the lines will be

parallel.

Parallel Lines 2

1. Draw line l and

point P not on l.

Parallel Lines 2

2. Draw a

transversal

through point P

intersecting line l.

Parallel Lines 2

3. Copy the angle

formed by the

transversal and

line l at point P.

Parallel Lines: Video

Click on the

image to

watch a

video of the

construction.

©2001 New York State Regents Exam Prep Center

Assignment

“Just Your Basic

Constructions

Worksheet:

• Parallel Lines 1 and 2

• Now on to the

“Construction

Problems” Worksheet