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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.
mathsConstruction / Practical Geometry (basics)Construction of Quadrilaterals

### Construction of Rectangles

In this page, a short and to-the-point overview of constructing rectangles is provided. It is outlined as follows.

•  Properties of rectangles is explained

•  The number of independent parameters in a rectangle is 1

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

click on the content to continue..

What is a rectangle?

• a parallelogram with all interior angles 90^@
• a parallelogram with all interior angles 90^@
• a rectangle is not a parallelogram

The answer is "a parallelogram with all interior angles 90^@"

A quadrilateral is defined by 5 parameters. A Parallelogram is defined by 3 parameters. And for a rectangle, the following properties provide additional dependency of parameters.

•  all interior angles are 90^@

•  diagonals are equal and bisect

•  opposite sides are parallel and equal

•  two angles on diagonals are supplementary These properties cause one parameter to be dependent on other parameters and so, a rectangle is defined by 2 parameters.

To construct a rectangle, 2 sides (bar(AB), bar(BC)) are given. This is illustrated in the figure. Which of the following helps to construct the specified rectangle?

• Consider this as two SAS triangles ABC and BAD
• Consider this as two SAS triangles ABC and BAD
• Consider this as two RHS triangles ABC and ACD

The answer is "Consider this as two SAS triangles ABC and ABD".

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

• Consider this as two SAS triangles ABC and BAD
• Consider this as two RHS triangles ABC and ACD
• Consider this as two RHS triangles ABC and ACD

The answer is "Consider this as two RHS triangles ABC and ABD".

To construct a rectangle, the diagonal (bar(AC)) and the angle between them (/_DOC) are given. This is illustrated in the figure. Which of the following helps to construct the specified rectangle?

• Consider this as two SAS triangles COD and AOB
• Consider this as two RHS triangles ABC and ABD
• Consider this as two RHS triangles ABC and ABD

The answer is "Consider this as two SAS triangle COD and AOB". Note: Use the property that diagonals bisect and mark the vertices at half diagonals.

Construction of Rectangles :

Properties of rectangle

•  all interior angles are 90^@

•  diagonals are equal and bisect

•  opposite sides are parallel and equal The formulations of questions

•  2 sides

•  1 side and the diagonal

•  the diagonal and an angle between the diagonals

use properties to figure out dependent parameters and look for triangles

slide-show version coming soon