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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 quadrilaterals is provided. It is outlined as follows.

 •  Properties of quadrilaterals is explained

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

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



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In a quadrilateral,

 •  sum of all interior angles is `360^@`. A quadrilateral is made of two triangles sharing one side. Each triangle is defined by `3` parameters and since they share a side, one parameter is common in the two sets of `3` parameters. quadrilateral introduction A quadrilateral is defined by `5` parameters.

To construct a quadrilateral, 4 sides (`bar(AB)`, `bar(BC)`, `bar(CD)`, `bar(AD)` ) and a diagonal (`bar(AC)`) are given. This is illustrated in the figure.quadrilateral construction 4 sides and 1 diagonal Which of the following helps to construct the specified quadrilateral?

  • consider this as two SSS triangles `ABC` and `ACD`
  • consider this as two SSS triangles `ABC` and `ACD`
  • the quadrilateral cannot be constructed

The answer is "consider this as two SSS triangles `ABC` and `ACD`"

To construct a quadrilateral, 4 (`bar(AB)`, `bar(BC)`, `bar(CD)`, `bar(AD)` ) sides and an angle (`/_B`) are given. This is illustrated in the figure. quadrilateral construction 4 sides and 1 angle Which of the following helps to construct the specified quadrilateral?

  • consider this as two SSS triangles `ABC` and `ACD`
  • consider this as an SAS triangle `ABC` and another SSS triangle `ACD`
  • consider this as an SAS triangle `ABC` and another SSS triangle `ACD`

The answer is "consider this as an SAS triangle `ABC` and another SSS triangle `ACD`"

To construct a quadrilateral, `3` (`bar(AB)`, `bar(BC)`, `bar(AD)` ) sides and two diagonals (`bar(AC)`, `bar(BD)`) are given. This is illustrated in the figure. quadrilateral construction 3 sides and 2 diagonals Which of the following helps to construct the specified quadrilateral?

  • consider this as two SSS triangles `ABC` and `ABD`
  • consider this as two SSS triangles `ABC` and `ABD`
  • consider this as an SAS triangle `ABC` and another SSS triangle `ACD`

The answer is "consider this as two SSS triangles `ABC` and `ABD`"

To construct a quadrilateral, `3` sides (`bar(AB)`, `bar(BC)`, `bar(AD)` ) and `2` angles (`/_A`, `/_B`) are given. This is illustrated in the figure. quadrilateral construction 3 sides and 2 angles Which of the following helps to construct the specified quadrilateral?

  • consider this as two SAS triangles `ABC` and `BAD`
  • consider this as two SAS triangles `ABC` and `BAD`
  • consider this as an SAS triangle `ABC` and another SSS triangle `ACD`

The answer is "consider this as two SAS triangles `ABC` and `BAD`"

To construct a quadrilateral, `2` sides (`bar(AB)`, `bar(BC)` ) and `3` angles (`/_A`, `/_B`, `/_C`)are given. This is illustrated in the figure. quadrilateral construction 2 sides and 3 angles Which of the following helps to construct the specified quadrilateral?

  • consider this as two SAS triangles `ABC` and `BAD`
  • consider this as an SAS triangle `ABC` and another ASA triangle with angles `/_C` and `/_A`
  • consider this as an SAS triangle `ABC` and another ASA triangle with angles `/_C` and `/_A`

The answer is "consider this as an SAS triangle `ABC` and another ASA triangle with two angles `/_C` and `/_A`". Note that `/_\ACD` is formed by angles `/_C` and `/_A`

Construction of Quadrilateral : Properties of quadrilaterals

 •  sum of interior angles `360^@`quadrilateral introduction The formulations of questions

 •  4 sides and a diagonal

 •  3 sided and 2 diagonals

 •  4 sides and an angle

 •  3 sides and 2 angles

 •  2 sides and 3 angles

                            
slide-show version coming soon