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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 rectangles is provided. It is outlined as follows.

 •  Properties of rectangles is explained

 •  The number of independent parameters in a rectangle is `1`

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



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What is a rectangle?rectangle introduction

  • a parallelogram with all interior angles `90^@`
  • a parallelogram with all interior angles `90^@`
  • a rectangle is not a parallelogram

The answer is "a parallelogram with all interior angles `90^@`"

A quadrilateral is defined by `5` parameters. A Parallelogram is defined by `3` parameters. And for a rectangle, the following properties provide additional dependency of parameters.

 •  all interior angles are `90^@`

 •  diagonals are equal and bisect

 •  opposite sides are parallel and equal

 •  two angles on diagonals are supplementaryrectangle introduction These properties cause one parameter to be dependent on other parameters and so, a rectangle is defined by `2` parameters.

To construct a rectangle, `2` sides (`bar(AB)`, `bar(BC)`) are given. This is illustrated in the figure.rectangle construction 2 sides Which of the following helps to construct the specified rectangle?

  • Consider this as two SAS triangles `ABC` and `BAD`
  • Consider this as two SAS triangles `ABC` and `BAD`
  • Consider this as two RHS triangles `ABC` and `ACD`

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

To construct a rectangle, a side (`bar(AB)`) and the diagonal (`bar(AC)`) are given. This is illustrated in the figure.rectangle construction a side and the diagonal Which of the following helps to construct the specified rectangle?

  • Consider this as two SAS triangles `ABC` and `BAD`
  • Consider this as two RHS triangles `ABC` and `ACD`
  • Consider this as two RHS triangles `ABC` and `ACD`

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

To construct a rectangle, the diagonal (`bar(AC)`) and the angle between them (`/_DOC`) are given. This is illustrated in the figure.rectangle construction a side and the diagonal Which of the following helps to construct the specified rectangle?

  • Consider this as two SAS triangles `COD` and `AOB`
  • Consider this as two RHS triangles `ABC` and `ABD`
  • Consider this as two RHS triangles `ABC` and `ABD`

The answer is "Consider this as two SAS triangle `COD` and `AOB`". Note: Use the property that diagonals bisect and mark the vertices at half diagonals.

Construction of Rectangles :

Properties of rectangle

 •  all interior angles are `90^@`

 •  diagonals are equal and bisect

 •  opposite sides are parallel and equalrectangle introduction The formulations of questions

 •  `2` sides

 •  `1` side and the diagonal

 •  the diagonal and an angle between the diagonals

use properties to figure out dependent parameters and look for triangles

                            
slide-show version coming soon