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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 Triangles (Fundamental Shape of Polygons)

### Fundamentals of Construction : Triangles

This lesson gives a short overview of triangles. Three parameters define a triangle and the following possible combinations uniquely define a triangle

•  Side-Side-Side (SSS)

•  Side-Angle-Side (SAS)

•  Angle-Side-Angle (ASA)

•  right angle-hypotenuse-side (RHS)

•  side-angle-altitude (SAL)

This set of parameters are given to construct a triangle.

click on the content to continue..

Triangle /_\ ABC has the following measurements as the parameters

•  side bar(AB)

•  side bar(BC)

•  side bar(CA)

•  angle /_A

•  angle /_B

•  angle /_C

•  altitude or height of triangle bar(CH) = l

Note that the three angles are not truly independent as /_A + /_B + /_C = 180^@

These are 7 parameters in total. How many independent parameters define a triangle?

• 7
• 3
• 3

The answer is "3". 3 independent parameters define a triangle. Other parameters can be derived from the given three parameters.

Considering that triangles are defined by three independent parameters, one of the following possible combination is provided to construct a particular triangle.

•  Side-Side-Side

•  Side-Angle-Side

•  Angle-Side-Angle

•  right angle-hypotenuse-side

•  side-angle-altitude

angle-angle-angle is just two independent parameters as the sum of angles are 180^@.

side-angle-angle is same as angle-side-angle, as the sum of interior angles property defines the third angle.

side-side-angle is ambiguous with two possible triangles, unless the given angle is 90^@ or obtuse

side-side-altitude is ambiguous with two possible triangles, unless it is right-triangle
The given parameters have to satisfy properties of a triangle.

eg1: 4,4,10 cm cannot be sss of a triangle, as sum of any two sides of a triangle has to be greater than the third side.

eg2: 200^@ cannot be an interior angle of a triangle, as sum of angles has to be 180^@

Defining a Triangle : Three parameters define a triangle and the following possible combinations uniquely define a triangle  •  Side-Side-Side (SSS)

•  Side-Angle-Side (SAS)

•  Angle-Side-Angle (ASA)

•  right angle-hypotenuse-side (RHS)

•  side-angle-altitude (SAL)

In practical geometry, we study construction of various figures using a scale, protractor, compass, and set-squares. Using these instruments, some fundamental elements of construction are realized. What are the fundamental elements of practical geometry?

• constructing a line, an arc, an angle, and a parallel
• constructing collinear points, equidistant points, equiangular points, and parallel points.
• both the above
• both the above

The answer is "both the above"

To construct any shape, the fundamental elements we use are  •  Construct a line passing through the two given points using a ruler or scale (collinear points)

•  Construct a ray at the given angle using a protractor (equiangular points)

•  Construct an arc at the given distance using a compass and a ruler or scale (equidistant points)

•  construct a parallel line using a set-square and a scale or another set-square. (points on a parallel)

slide-show version coming soon