Construction (Geometry)
See how to construct a line segment/angle
by using a compass and a ruler.
6 examples and their solutions.
Construction: Midpoint of a Line Segment
Example
Construct the midpoint of the given line segment.
Solution Place the point of the compass at 1.
Draw two arcs
on the top and bottom of the segment.
Set the radius of the compass
that seems to be larger than
one half the length of the segment.
Draw two arcs
on the top and bottom of the segment.
Set the radius of the compass
that seems to be larger than
one half the length of the segment.
↓
Without changing the radius of the compass,
place the point of the compass at 2.
place the point of the compass at 2.
↓
Draw two arcs that pass through 3 and 4.
↓
Draw a line that passes through 3 and 4.
↓
The brown point is the midpoint
of the line segment.
of the line segment.
And the blue line is the perpendicular bisector
of the line segment.
of the line segment.
Close
Construction: Congruent Angle
Example
Construct an angle on the right ray
that is congruent to the left angle.
Solution that is congruent to the left angle.
Place the point of the compass at 1.
Draw an arc that passes through both rays.
Draw an arc that passes through both rays.
↓
Without changing the radius of the compass,
place the point of the compass at 2.
place the point of the compass at 2.
↓
Draw an arc (blue arc)
just like the previous arc.
just like the previous arc.
↓
Place the point of the compass at 3.
Set the radius of the compass 3 ~ 4.
Set the radius of the compass 3 ~ 4.
↓
Without changing the radius of the compass,
place the point of the compass at 5.
place the point of the compass at 5.
↓
Draw an arc that passes through 6.
↓
Draw a ray that passes through 6.
↓
Then the right side angle
is congruent to the left side angle.
is congruent to the left side angle.
Close
Construction: Angle Bisector
Example
Construct an angle bisector of the given angle.
Solution Place the point of the compass at 1.
Draw an arc that passes through both rays.
Draw an arc that passes through both rays.
↓
Place the point of the compass at 2.
Draw an arc
that seems to pass the middle of the angle.
Draw an arc
that seems to pass the middle of the angle.
↓
Without changing the radius of the compass,
place the point of the compass at 3.
place the point of the compass at 3.
↓
Draw an arc that passes through 4.
↓
Draw a ray that starts at 1
and that passes through 4.
and that passes through 4.
↓
Then the blue ray
is the angle bisector of the given angle.
is the angle bisector of the given angle.
Close
Construction: Perpendicular Line from a Point on the Line
Example
Construct a perpendicular line
that passes through the point on the line.
Solution that passes through the point on the line.
Place the point of the compass at 1.
Draw two arcs
that intersect with the given line.
Draw two arcs
that intersect with the given line.
↓
Place the point of the compass at 2.
Draw two arcs
on the top and bottom of the given point.
Draw two arcs
on the top and bottom of the given point.
↓
Without changing the radius of the compass,
place the point of the compass at 3.
place the point of the compass at 3.
↓
Draw two arcs that pass through 4 and 5.
↓
Draw a line that passes through 4 and 5.
↓
The blue line is the perpendicular line
that passes through the point on the given line.
that passes through the point on the given line.
Close
Construction: Perpendicular Line from a Point Not on the Line
Example
Construct a perpendicular line
that passes through the point not on the line.
Solution that passes through the point not on the line.
Place the point of the compass at 1.
Draw two arcs
that intersect with the given line.
Draw two arcs
that intersect with the given line.
↓
Place the point of the compass at 2.
Draw an arc
that is below the given point.
Draw an arc
that is below the given point.
↓
Without changing the radius of the compass,
place the point of the compass at 3.
place the point of the compass at 3.
↓
Draw an arc that passes through 4.
↓
Draw a line that passes through 1 and 4.
↓
The blue line is the perpendicular line
that passes through the point
not on the given line.
that passes through the point
not on the given line.
Close
Constuction: Parallel Line
Example
Construct a line
that is parallel to the given line
and that passes through the given point not on the line.
Solution that is parallel to the given line
and that passes through the given point not on the line.
Draw a line
that passes through
the given line and the given point 1.
that passes through
the given line and the given point 1.
↓
Place the point of the compass at 2.
Draw an arc that passes through 3 and 4.
Draw an arc that passes through 3 and 4.
↓
Without changing the radius of the compass,
place the point of the compass at 1.
place the point of the compass at 1.
↓
Draw an arc
just like the previous arc.
just like the previous arc.
↓
Place the point of the compass at 3.
Set the radius of the compass 3 ~ 4.
Set the radius of the compass 3 ~ 4.
↓
Without changing the radius of the compass,
place the point of the compass at 5.
place the point of the compass at 5.
↓
Draw an arc that passes through 6.
↓
Draw a line that passes through 1 and 6.
↓
Then the blue line is a parallel line
that passes through the given point.
that passes through the given point.
Close