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

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.