__maths__>__Construction / Practical Geometry (basics)__>__Secondary Elements of Practical Geometry__### Perpendicular Bisector to a Line Segment

In this page, a short and to-the-point overview of constructing a bisector to a line segment is provided.

*click on the content to continue..*

What is a rhombus?

- A four sided figure with all sides equal
- A four sided figure with all sides equal
- not a figure

The answer is "A four sided figure with all sides equal"

A rhombus has the following properties. • All sides are equal (and parallel)

• *the diagonals perpendicularly bisect*

• opposite angles are equal

• adjacent angles are supplementary

Which of the following geometrical properties help to construct a perpendicular bisector to a line?

- diagonals of rhombus perpendicularly bisect
- diagonals of rhombus perpendicularly bisect
- sides of a rhombus are equal in length

The answer is "diagonals of rhombus perpendicularly bisect"

Given line segment `bar(AB)`. The perpendicular bisector `bar(pq)` is to be constructed. • Take a compass

• fix a random distance between tips

• construct arcs from position `A` above and below `bar(AB)`

• construct arcs from position `B` above and below `bar(AB)`

• the intersecting points are `P` and `Q`.

Note that the distance between tips of the compass is not modified and so, the sides `bar(AP)`, `bar(PB)`, `bar(BQ)`, and `bar(QA)` form a rhombus. From the property of a rhombus, the diagonals `bar(AB)` and `bar(PQ)` perpendicularly bisect each other.*Note for curious students: It can be a kite, with `bar(AB)` as minor diagonal. Property of a kite, the major diagonal `bar(PQ)` bisects minor diagonal `bar(AB)`. *

**Bisecting a Line Segment** : Use a compass to mark a rhombus with the given line segment as one of the diagonals. The perpendicular bisector is the other diagonal.

*slide-show version coming soon*