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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 Trapezium

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

•  Properties of trapezium is explained

•  The number of independent parameters in a trapezium is 4

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

click on the content to continue..

What is a trapezium?

• A parallelogram with two pairs of parallel sides
• A quadrilateral with one pair of parallel sides
• A quadrilateral with one pair of parallel sides

Quadrilateral is defined by 5 parameters. In a trapezium, the following property provides dependence of parameters

•  one pair of sides are parallel

Note: The sides that are parallel are called bases. The other two sides are referred as sides.A trapezium is defined by 4 parameters.

To construct a trapezium, 2 bases (bar(AB), bar(CD)) , 1 diagonal (bar(AC)) and 1 side (bar(BC)) are given. This is illustrated in the figure Which of the following helps to construct the specified trapezium?

• consider as an SSS triangle ABC and mark D on a parallel
• consider as an SSS triangle ABC and mark D on a parallel
• consider as an ASA triangle ABC and mark D on a ray

The answer is "consider as an SSS triangle in ABC and mark D on a parallel"

To construct a trapezium, 2 bases (bar(AB), bar(CD)), 1 side (bar(BC)), and an angle (/_B) are given. This is illustrated in the figure Which of the following helps to construct the specified trapezium?

• consider as as SAS triangle in ABC and mark D on a parallel
• consider as as SAS triangle in ABC and mark D on a parallel
• consider as a ASA triangle in ABC and mark D on a ray

The answer is "consider as a SAS triangle in ABC and mark D on a parallel"

To construct a trapezium, 2 bases (bar(AB), bar(CD)), a diagonal (bar(AC)), and the angle between diagonal and the base (/_CAB)are given. This is illustrated in the figure Which of the following helps to construct the specified trapezium?

• consider as a SAS triangle CAB and mark D on a parallel
• consider as a SAS triangle CAB and mark D on a parallel
• consider as a ASA triangle ABC and mark D on a ray

The answer is "consider as a SAS triangle in CAB and mark D on a parallel"

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

• consider as an SSS triangle ABC
• consider as an SAS triangle ABC and construct ray AD to mark D on a parallel
• consider as an SAS triangle ABC and construct ray AD to mark D on a parallel

The answer is "consider as a SAS triangle in ABC and construct ray AD to mark D on a parallel"

Construction of Trapezium :

Properties of trapezium:

•  one pair of sides are parallel

Note: The sides that are parallel are called bases. The other two sides are referred as sides. The formulations of questions

•  2 bases, 1 side, 1 diagonal

•  2 bases, 1 diagonal, 1 angle between one base and the given diagonal

•  2 bases, 1 side, 1 angle between one base and given side

•  1 base, 2 angles on the given base, 1 diagonal

use properties to figure out dependent parameters and look for triangles.

slide-show version coming soon