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mathsConstruction / Practical Geometry (High)Construction of Triangles with Secondary Information

### Construction of Triangles With Secondary Information

Triangles are define by 3 independent parameters. Usually, the three independent parameters are chosen from 6 primary parameters -- the three sides and the three angles.

The sum of two sides, or perimeter of the triangle, etc. are secondary parameters.

If one or more of given parameters is of secondary type, then how to construct the specified triangle? A short overview of approaching such problems is provided in this lesson.

click on the content to continue..

Earlier we studied about construction of triangles. To construct a triangle, one of the following set of parameters is provided.

•  side-side-side

•  side-angle-side

•  angle-side-angle

What is common in the given properties?

• all parameters directly provide one of 3 sides or 3 angles
• all parameters directly provide one of 3 sides or 3 angles
• nothing common is observed

The answer is "all parameters directly provide one of 3 sides or 3 angles".

A triangle has 3 sides and 3 angles. But a triangle is defined by only three parameters. These parameters are basic parameters.

Examples of "derived" parameters are
sum of two sides
difference between two sides
perimeter of the triangle

If the following are provided, how to construct the triangle?
side-angle-sum of two sides
side-angle-difference between two sides
perimeter-angle-angle

With trigonometry or with coordinate geometry, the given parameters can be converted to basic parameters. But, the objective of geometrical construction is to figure out the shape (the triangle) without any calculations.

In this lesson, construction of triangles with derived or secondary parameters is explained.

slide-show version coming soon