6th Grade Math Textbook, Fundamentals

 &KDSWHU

9-6

Line Constructions

Objective To construct a line perpendicular to a given line

through a given point on that line • To construct a line perpendicular

to a given line through a given point not on that line • To construct

a line parallel to a given line through a given point

You are drawing a plan for a proposed shopping mall next to a
housing development. You need to draw parallel and perpendicular
lines to show streets and mall entrances and exits. The only tools you
have are a pencil, a straightedge, and a compass. How can you use
these tools to complete the constructions needed?

To construct a line perpendicular to a given line

through a point onthat line:

Draw a line through a point P.

With your compass point on P, draw two arcs

intersecting line at two points on opposite sides of

point P. Label those points Aand B.

Widen the compass to construct two intersecting

arcs above point P, one with the compass point at A,

and the other with the compass point at B. Label the

intersection of the arcs as point C. Draw CP.

CP⊥line 

To construct a line perpendicular to a given line

through a given point not onthe line:

Draw a line m.Draw a point Pat a location not on line m.

With your compass point on P, draw an arc

intersecting line mat two points. Label those points

Aand B.

Using the samecompass setting, construct two

intersecting arcs below line segment AB, one with

the compass point at A, and the other with the

compass point at B. Label the intersection of the

arcs as point Q. Draw QP.

QP⊥line m



ABP

C

m

P

m

AB

P

m

AB

Q

P



P



ABP