__maths__>__Construction / 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.

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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. 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*