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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 Kite

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

•  Properties of kites is explained

•  The number of independent parameters in a kite is 1

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

click on the content to continue..

What is a kite?

• kite is not a quadrilateral

A quadrilateral is defined by 5 parameters. For a kite, the following properties provide additional dependency of parameters

•  two pair of equal sides

•  major diagonal perpendicularly bisects the minor diagonal. the diagonal that divides the kite into two congruent triangles is called major. The other diagonal is the minor diagonal.

•  major diagonal bisects the angles at the vertices

•  two equal opposite angles and two unequal opposite angles -- all sum up to 360^@ A kite is defined by 3 parameters.

To construct a kite, 2 unequal sides (bar(AB), bar(BC)) and the angle between them (/_B) are given. This is illustrated in the figure Which of the following helps to construct the specified kite?

• Consider as an SAS triangle in BAD and an SSS triangle BCD
• Consider as an SAS triangle in BAD and an SSS triangle BCD
• Consider as two ASA triangles in BAD and BCD

The answer is "Consider as an SAS triangle in BAD and SSS triangle BCD"

To construct a kite, a side (bar(AB)) and 2 angles (/_A,/_B) are given. This is illustrated in the figure Which of the following helps to construct the specified kite?

• Consider as an SAS triangle in ABC and an ASA triangle ACD
• Consider as an SAS triangle in ABC and an ASA triangle ACD
• Consider as two ASA triangles in ABC and ACD

The answer is "Consider as an SAS triangle in ABC and ASA triangle ACD"

To construct a kite, 2 unequal sides (bar(AB), bar(BC)) and the major diagonal (bar(BD)) are given. This is illustrated in the figure Which of the following helps to construct the specified kite?

• Consider as two SSS triangles in ABD and BDC
• Consider as two SSS triangles in ABD and BDC
• Consider as two ASA triangles in BAD and BCD

The answer is "Consider as two SSS triangles in ABD and BDC"

To construct a kite, 2 unequal sides (bar(AB), bar(BC)) and the minor diagonal (bar(AC)) are given. This is illustrated in the figure Which of the following helps to construct the specified kite?

• Consider as two isosceles SSS triangles in ABC and ACD
• Consider as two isosceles SSS triangles in ABC and ACD
• Consider as two ASA triangles in BAD and BCD

The answer is "Consider as two isosceles SSS triangles in ABC and ACD"

To construct a kite, a side (bar(AB)), the major diagonal (bar(BD)), and angle (/_ABD) between them are given. This is illustrated in the figure Which of the following helps to construct the specified kite?

• Consider as two SSS triangles in ABC and ACD
• Consider as two SAS triangles in ABD and DBC
• Consider as two SAS triangles in ABD and DBC

The answer is "Consider as two SAS triangles in ABD and DBC"

Construction of Kite :

Properties of Kite:

•  two pair of equal sides

•  major diagonal perpendicularly bisects the minor diagonal. The diagonal that divides the kite as two congruent triangles is the major diagonal.

•  major diagonal bisects the angles at the vertices

•  two equal opposite angles and two unequal opposite angles sum up to 360^@ The formulations of questions

•  2 unequal sides and the angle between them

•  1 side and 2 angles

•  2 unequal sides and the major diagonal

•  2 unequal sides and the minor diagonal

•  1 side, major diagonal and the angle between them

slide-show version coming soon