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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.

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mathsConstruction / Practical Geometry (basics)Construction of Quadrilaterals

### Construction of Rhombus

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.

click on the content to continue..

What is a rhombus?

• 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 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 figure 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 figure 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 figure 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 supplementary 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.

slide-show version coming soon