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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

In this page, a short analysis of constructing triangles with the following is provided.

 •  angle-angle-side (equivalent to angle-side-angle)

 •  angle-angle-angle (only 2 parameters)

 •  side-side-angle (two possible triangles)

 •  side-side-altitude (two possible triangles)

 •  rightangle-angle-side (equivalent to angle-side-angle)



click on the content to continue..

To construct a triangle, "angle-angle-side" is provided.

Which of the following method can be used to construct?

  • this is equivalently "angle-side-angle" as sum of angle is `180^@`
  • this is equivalently "angle-side-angle" as sum of angle is `180^@`
  • the given "angle-angle-side" cannot be used to construct a triangle

The answer is "this is equivalently "angle-side-angle" as sum of angle is `180^@`".

To construct a triangle, "angle-angle-angle" is provided.

Which of the following method can be used to construct?

  • this is equivalently "side-side-side" and so the triangle can be constructed
  • the given angles are not `3` independent parameters
  • the given angles are not `3` independent parameters

The answer is "the given angles are not `3` independent parameters as given `2` angles the third angle is defined". The `3` angles together form `2` independent parameters.

To construct a triangle, "side-side-angle" is provided. triangle construction ssa Which of the following method can be used to construct?

  • the given information "side-side-angle" may lead to two possible solutions
  • the given information "side-side-angle" may lead to two possible solutions
  • the given information can be rewritten as "side-angle-side" and a triangle may be constructed

The answer is "the given information "side-side-angle" may lead to two possible solutions"

To construct a triangle, "side1-side2-angle" are provided. The top portion of the figure illustrates the construction.

 •  Side2 `bar(AB)` is constructed

 •  `/_A` is constructed with `vec(AP)`.

 •  side1 is to be constructed. With a compass from point `B`, an arc is drawn. This cuts at 2 points `C1` and `C2`. The triangles `/_\ ABC1` and `/_\ ABC2` both satisfy the given parameters

   `bar(AB)` is the given side2

   `/_A` is the given angle

   Both `bar(BC1)` and `bar(BC2)` equal side1.

Since this leads to two possible solutions, the triangle is not uniquely defined. triangle construction ssa Under some conditions, the given information "side1-side2-angle" leads to an unique triangle. This is illustrated in the lower part of the figure.

 •  when the given angle is obtuse, the side1 has to be greater than side2. This is illustrated in `/_\ ABC3`.

 •  when the side1 is greater than the side2. This is illustrated in `/_\ ABC4`

To construct a triangle, "side-side-altitude" are provided. triangle construction ssl Which of the following method can be used to construct?

  • the given information "side-side-altitude" may lead to two possible solutions
  • the given information "side-side-altitude" may lead to two possible solutions
  • the given information can be rewritten as "side-angle-side" and a triangle may be constructed

The answer is "the given information "side-side-altitude" may lead to two possible solutions"

To construct a triangle, "side1-side2-altitude" is provided. The figure illustrates possible construction.

 •  Side2 `bar(AB)` is constructed

 •  Parallel at altitude is constructed at point `E`.

 •  Side1 is to be constructed. With a compass from point `A`, an arc is drawn. This cuts at 2 points `C1` and `C2`.triangle construction ssl The triangle `/_\ ABC1` and `/_\ ABC2` both satisfy the given parameters

   `bar(AB)` is the given side2

   `bar(DE)` is the given altitude

   Both `bar(AC1)` and `bar(AC2)` equal side1.

Since this leads to two possible solutions, the given S A L does not uniquely define a triangle.

To construct a triangle, "right angle-angle1-side" are provided. Which of the following method can be used to construct?

  • it can be converted to "right angle-side-angle2" by sum of interior angle property
  • it can be converted to "right angle-side-angle2" by sum of interior angle property
  • an unique triangle cannot be constructed with the given info

The answer is "it can be converted to `right angle-side-angle2` by sum of interior angle property"

To construct a triangle, "right angle-angle1-hypotenuse" is provided. Which of the following method can be used to construct?

  • it can be converted to `angle1-hypotenuse-angle2` by sum of interior angle property
  • it can be converted to `angle1-hypotenuse-angle2` by sum of interior angle property
  • an unique triangle cannot be constructed with the given info

The answer is "it can be converted to `angle1-hypotenuse-angle2` by sum of interior angle property"

                            
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