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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.continue

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.



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What is a square?square introduction

  • 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 square introduction 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.square construction a side 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.square construction a diagonal 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^@`square introduction The formulations of questions

 •  `1` side

 •  `1` diagonal

use properties to figure out dependent parameters and look for triangles

                            
slide-show version coming soon