__maths__>__Construction / Practical Geometry (basics)__>__Construction of Triangles (Fundamental Shape of Polygons)__### Construction of Triangles with Other information

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. 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. 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. 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`. 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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