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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.

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.

click on the content to continue..

•  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. 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. 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. 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. 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. 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. 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

•  sum of interior angles 360^@ 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