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Thought-Process to Discover Knowledge

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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 trapezium is provided. It is outlined as follows.

 •  Properties of trapezium is explained

 •  The number of independent parameters in a trapezium is `4`

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



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What is a trapezium?trapezium introduction

  • A parallelogram with two pairs of parallel sides
  • A quadrilateral with one pair of parallel sides
  • A quadrilateral with one pair of parallel sides

The answer is "A quadrilateral with one pair of parallel sides"

Quadrilateral is defined by `5` parameters. In a trapezium, the following property provides dependence of parameters

 •  one pair of sides are parallel

Note: The sides that are parallel are called bases. The other two sides are referred as sides.trapezium introductionA trapezium is defined by `4` parameters.

To construct a trapezium, `2` bases (`bar(AB)`, `bar(CD)`) , `1` diagonal (`bar(AC)`) and `1` side (`bar(BC)`) are given. This is illustrated in the figureconstruction of trapezium with 2 bases, 1 diagonal, 1 side Which of the following helps to construct the specified trapezium?

  • consider as an SSS triangle `ABC` and mark `D` on a parallel
  • consider as an SSS triangle `ABC` and mark `D` on a parallel
  • consider as an ASA triangle `ABC` and mark `D` on a ray

The answer is "consider as an SSS triangle in `ABC` and mark `D` on a parallel"

To construct a trapezium, `2` bases (`bar(AB)`, `bar(CD)`), `1` side (`bar(BC)`), and an angle (`/_B`) are given. This is illustrated in the figureconstruction of trapezium with 2 bases, 1 side, and an angle Which of the following helps to construct the specified trapezium?

  • consider as as SAS triangle in `ABC` and mark `D` on a parallel
  • consider as as SAS triangle in `ABC` and mark `D` on a parallel
  • consider as a ASA triangle in `ABC` and mark `D` on a ray

The answer is "consider as a SAS triangle in `ABC` and mark `D` on a parallel"

To construct a trapezium, `2` bases (`bar(AB)`, `bar(CD)`), a diagonal (`bar(AC)`), and the angle between diagonal and the base (`/_CAB`)are given. This is illustrated in the figureconstruction of trapezium with 2 bases, 1 diagonal, and an angle Which of the following helps to construct the specified trapezium?

  • consider as a SAS triangle `CAB` and mark `D` on a parallel
  • consider as a SAS triangle `CAB` and mark `D` on a parallel
  • consider as a ASA triangle `ABC` and mark `D` on a ray

The answer is "consider as a SAS triangle in `CAB` and mark `D` on a parallel"

To construct a trapezium, a base(`bar(AB)`), a diagonal (`bar(AC)`), and `2` angles (`/_A`, `/_B`) on the given base are given. This is illustrated in the figureconstruction of trapezium with 1 base, 1 diagonal, and 2 angle Which of the following helps to construct the specified trapezium?

  • consider as an SSS triangle `ABC`
  • consider as an SAS triangle `ABC` and construct ray `AD` to mark `D` on a parallel
  • consider as an SAS triangle `ABC` and construct ray `AD` to mark `D` on a parallel

The answer is "consider as a SAS triangle in `ABC` and construct ray `AD` to mark `D` on a parallel"

Construction of Trapezium :

Properties of trapezium:

 •  one pair of sides are parallel

Note: The sides that are parallel are called bases. The other two sides are referred as sides.trapezium introduction The formulations of questions

 •  2 bases, 1 side, 1 diagonal

 •  2 bases, 1 diagonal, 1 angle between one base and the given diagonal

 •  2 bases, 1 side, 1 angle between one base and given side

 •  1 base, 2 angles on the given base, 1 diagonal

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

                            
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