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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.continue

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.



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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.triangles introduction 1 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
triangles introduction 1 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 triangletriangles introduction 1  •  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.4 fundamental elements of practical geometry 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 4 fundamental elements of practical geometry  •  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