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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 rhombus is provided. It is outlined as follows.

 •  Properties of rhombus is explained

 •  The number of independent parameters in a rhombus is `2`

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



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What is a rhombus?rhombus introduction

  • A parallelogram with all sides equal
  • A parallelogram with all sides equal
  • not a parallelogram

The answer is "A parallelogram with all sides equal"

A quadrilateral is defined by `5` parameters. A parallelogram is defined by `3` parameters. And in a rhombus, the following properties provide additional dependency of parameters

 •  All sides are equal (and parallel)

 •  the diagonals perpendicularly bisect

 •  opposite angles are equal

 •  adjacent angles are supplementary rhombus introduction These properties cause one parameter dependent on other parameters and effectively, a rhombus is defined by `2` parameters.

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

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

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

To construct a rhombus, a side (`bar(AB)`) and an angle (`/_B`) are given. This is illustrated in the figureconstruction rhombus a side and an angle Which of the following helps to construct the specified rhombus?

  • With a side and an angle, a rhombus cannot be constructed
  • Consider this as two SAS triangles `ABC` and `BAD`
  • Consider this as two SAS triangles `ABC` and `BAD`

The answer is "Consider this as two SAS triangles `ABC` and `BAD`". Use the property `/_A + /_B = 180^@` to find the second angle.

To construct a rhombus, two diagonals (`bar(AC)`, `bar(BD)`) are given. This is illustrated in the figureconstruction rhombus two diagonals Which of the following helps to construct the specified rhombus?

  • With the two diagonals, a rhombus cannot be constructed
  • Consider this as two SAS triangles `DOC` and `AOB` with diagonals perpendicularly bisecting
  • Consider this as two SAS triangles `DOC` and `AOB` with diagonals perpendicularly bisecting

The answer is "Consider this as two SAS triangles `DOC` and `AOB`". Use the property that the diagonals perpendicularly bisect and mark the vertices at half diagonals.

Construction of Rhombus :

Properties of Rhombus

 •  All sides are equal (and parallel)

 •  the diagonals perpendicularly bisect

 •  opposite angles are equal

 •  adjacent angles are supplementaryrhombus introduction The formulations of questions

 •  `1` side and `1` diagonal

 •  `1` side and `1` angle

 •  `2` diagonals

use properties to figure out dependent parameters and look for triangles.

                            
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