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.