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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.

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mathsConstruction / Practical Geometry (basics)Construction of Quadrilaterals

### Construction of Parallelograms

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

•  Properties of parallelograms is explained

•  The number of independent parameters in a parallelogram is 3

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

click on the content to continue..

What is a parallelogram?

• a quadrilateral with two pairs of parallel sides
• a quadrilateral with two pairs of parallel sides

Quadrilateral is defined by 5 parameters. In a parallelogram, the following properties provide dependency of parameters

•  opposite sides are parallel and that makes them equal

•  opposite angles are equal

•  diagonals bisect

•  two angles on diagonals are supplementary These properties cause two parameters to be dependent on other parameters and so, a parallelogram is defined by 3 parameters.

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

• Consider this as two SSS triangles ABC and ACD
• Consider this as two SSS triangles ABC and ACD
• Consider this as an SSS triangle ABC and another SAS triangle ABD

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

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

• Consider this as two SSS triangles ABC and ABD
• 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 a SAS triangles ABC and another SSS triangle ACD".

Note: Once the first SAS triangle ABC is completed, the bar(AC) is fixed. Using that SSS triangle ACD is constructed.

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

• Consider this as two SSS triangles ABC and ACD
• Consider this as an SSA triangle ABC and an SSS triangle ACD
• Consider this as an SSA triangle ABC and an SSS triangle ACD

The answer is "Consider this as an SSA triangles ABC and an SSS triangle ACD".

Note: Once the first SAS triangle ABC is completed, that triangle can be copied to a SSS triangle ACD.

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

• With a side and two diagonals, a parallelogram cannot be constructed
• Consider this as an SSS triangle AOB. Then construct points C and D
• Consider this as an SSS triangle AOB. Then construct points C and D

The answer is "Consider this as an SSS triangles AOB. Then construct points C and D".

Note: The diagonals bisect, and AOB is constructed with half-diagonals. The vec(AO) and vec(BO) are extended. The half diagonals are marked from point O to construct vertices C and D

To construct a parallelogram, two diagonals (bar(AC), bar(BD)) and the angle between diagonals (/_AOB) are given. This is illustrated in the figure. Which of the following helps to construct the specified parallelogram?

• With two diagonals and angle between them, a parallelogram cannot be constructed
• Consider this as two SAS triangles DOC and AOB
• Consider this as two SAS triangles DOC and AOB

The answer is "Consider this as two SAS triangles DOC and AOB".

Note: Draw line AOC where points A and C are marked with half diagonal from point O. At the given angle line BOD is drawn and points B and D are marked.

Construction of Parallelograms :

Properties of Parallelograms

•  opposite sides are parallel and equal

•  opposite angles are equal

•  diagonals bisect

•  two angles on diagonals are supplementary The formulations of questions

•  2 sides and 1 diagonal

•  2 sides and 1 angle

•  1 side, 1 diagonal and 1 angle

•  1 side and 2 diagonals

•  2 diagonals and 1 angle between diagonals

use properties to figure out dependent parameters and look for triangles

slide-show version coming soon