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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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mathsConstruction / 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

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