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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.

Read in the blogs more about the unique learning experience at nubtrek.
mathsConstruction / Practical Geometry (basics)Construction of Quadrilaterals

### Construction of Square

In this page, a short and to-the-point overview of constructing squares is provided. It is outlined as follows.

•  Properties of squares is explained

•  The number of independent parameters in a square is 1

•  For a given parameter, construction of squares is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of squares.

click on the content to continue..

What is a square?

• a rectangle with all sides equal
• a rectangle with all sides equal
• a square is not a rectangle

The answer is "a rectangle with all sides equal"

A rectangle is defined by 2 parameters. And in a square, the following properties provide additional dependency of parameters.

•  all sides are equal

•  diagonals are equal and perpendicularly bisect

•  opposite sides are parallel

•  all interior angles are 90^@

•  two angles on diagonals are supplementary These properties cause one parameter to be dependent on other parameters and so, a square is defined by 1 parameter.

To construct a square, the side (bar(AB)) is given. This is illustrated in the figure. Which of the following helps to construct the specified square?

• Consider this as two SAS triangles ABC and ABD
• Consider this as two SAS triangles ABC and ABD
• Consider this as two RHS triangles ABC and ACD

The answer is "Consider this as two SAS triangles ABC and ABD".

To construct a square, the diagonal (bar(AC)) is given. This is illustrated in the figure. Which of the following helps to construct the specified square?

• Mark the vertices at half diagonals on perpendicular lines
• Mark the vertices at half diagonals on perpendicular lines
• Consider this as two RHS triangles ABC and ACD

The answer is "Consider as two SAS triangles and Mark the vertices at half diagonals on perpendicular lines". Use the property that diagonals bisect.

Construction of Square :

Properties of Square:

•  all sides are equal

•  diagonals are equal and perpendicularly bisect

•  opposite sides are parallel

•  all interior angles are 90^@ The formulations of questions

•  1 side

•  1 diagonal

use properties to figure out dependent parameters and look for triangles

slide-show version coming soon