Construction of Triangle(RHS)
In this page, a short and to-the-point overview of constructing triangles with right-angle-hypotenuse-side (a right-triangle) is provided.
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To construct a triangle, "right angle-side-hypotenuse" is provided. Which of the following is equivalently the given information?
Note: The third side of a right triangle can be calculated using Pythagorean theorem. But, in construction problems, the objective is to construct without complex geometrical calculations involving square-root.
- none of the above
The answer is "angle-side-side".
Note the order of the given parameters matters. For example, `3cm-60^@-4cm` is different from `60^@-3cm-4cm`.
To construct a triangle `/_\ ABC` with given "right angle-side-hypotenuse" `4`cm and `5`cm • Construct a line and mark side `bar(AB)` with a compass measuring `4`cm
• measure `90^@` angle and draw a ray from point `A`
• measure `bar(BC)` `5`cm in a compass and draw an arc from point `B` cutting the ray
• the arc and the ray cut at point `C`. Connect the point to point `B` to get `bar(BC)`
`/_\ ABC` is constructed.
There are few things to note in construction of "rhs". Note 1: The method is called either as "rhs" or "rsh".
Note 2: In other formats, the order of the given parameters matter. For example in "sas", the given angle is subtended by the given two sides. In "rhs" the there parameters are not given in order, but are connected by the properties of right-triangles. Among the two given sides, the longer one is the hypotenuse.
Note 3: If the angle is not right-angle, then "angle-side-side" may (under some conditions) lead to two possible triangles. This is explained later.
Construction of RHS triangle :
use compass to the measure lengths and protractor to measure the given angle. Once the vertices are marked, join them to form the triangle.