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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 parallelograms is provided. It is outlined as follows.

 •  Properties of parallelograms is explained

 •  The number of independent parameters in a parallelogram is `3`

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



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What is a parallelogram? parallelogram introduction

  • a quadrilateral with two pairs of parallel sides
  • a quadrilateral with two pairs of parallel sides
  • not a quadrilateral

The answer is "a quadrilateral with two pair of parallel sides"

Quadrilateral is defined by `5` parameters. In a parallelogram, the following properties provide dependency of parameters

 •  opposite sides are parallel and that makes them equal

 •  opposite angles are equal

 •  adjacent angles are supplementary

 •  diagonals bisect

 •  two angles on diagonals are supplementaryparallelogram introduction These properties cause two parameters to be dependent on other parameters and so, a parallelogram is defined by `3` parameters.

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

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

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

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

  • Consider this as two SSS triangles `ABC` and `ABD`
  • 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 a SAS triangles `ABC` and another SSS triangle `ACD`".

Note: Once the first SAS triangle `ABC` is completed, the `bar(AC)` is fixed. Using that SSS triangle `ACD` is constructed.

To construct a parallelogram, a diagonal (`bar(AC)`), a side (`bar(AB)`), and an obtuse angle (`/_B`) are given. This is illustrated in the figure. parallelogram construction a diagonal, a sides, and an angle Which of the following helps to construct the specified parallelogram?

  • Consider this as two SSS triangles `ABC` and `ACD`
  • Consider this as an SSA triangle `ABC` and an SSS triangle `ACD`
  • Consider this as an SSA triangle `ABC` and an SSS triangle `ACD`

The answer is "Consider this as an SSA triangles `ABC` and an SSS triangle `ACD`".

Note: Once the first SAS triangle `ABC` is completed, that triangle can be copied to a SSS triangle `ACD`.

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

  • With a side and two diagonals, a parallelogram cannot be constructed
  • Consider this as an SSS triangle `AOB`. Then construct points `C` and `D`
  • Consider this as an SSS triangle `AOB`. Then construct points `C` and `D`

The answer is "Consider this as an SSS triangles `AOB`. Then construct points `C` and `D`".

Note: The diagonals bisect, and `AOB` is constructed with half-diagonals. The `vec(AO)` and `vec(BO)` are extended. The half diagonals are marked from point `O` to construct vertices `C` and `D`

To construct a parallelogram, two diagonals (`bar(AC)`, `bar(BD)`) and the angle between diagonals (`/_AOB`) are given. This is illustrated in the figure. parallelogram construction 2 diagonals and angle Which of the following helps to construct the specified parallelogram?

  • With two diagonals and angle between them, a parallelogram cannot be constructed
  • Consider this as two SAS triangles `DOC` and `AOB`
  • Consider this as two SAS triangles `DOC` and `AOB`

The answer is "Consider this as two SAS triangles `DOC` and `AOB`".

Note: Draw line `AOC` where points `A` and `C` are marked with half diagonal from point `O`. At the given angle line `BOD` is drawn and points `B` and `D` are marked.

Construction of Parallelograms :

Properties of Parallelograms

 •  opposite sides are parallel and equal

 •  opposite angles are equal

 •  adjacent angles are supplementary

 •  diagonals bisect

 •  two angles on diagonals are supplementary parallelogram introduction The formulations of questions

 •  `2` sides and `1` diagonal

 •  `2` sides and `1` angle

 •  `1` side, 1 diagonal and `1` angle

 •  `1` side and `2` diagonals

 •  `2` diagonals and `1` angle between diagonals

use properties to figure out dependent parameters and look for triangles

                            
slide-show version coming soon