__maths__>__Construction / Practical Geometry (basics)__>__Construction of Quadrilaterals__### Construction of Quadrilaterals

In this page, a short and to-the-point overview of constructing quadrilaterals is provided. It is outlined as follows.

• Properties of quadrilaterals is explained

• The number of independent parameters in a quadrilateral is `1`

• For a given parameter, construction of quadrilaterals is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of quadrilaterals.

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In a quadrilateral,

• sum of all interior angles is `360^@`. A quadrilateral is made of two triangles sharing one side. Each triangle is defined by `3` parameters and since they share a side, one parameter is common in the two sets of `3` parameters. A quadrilateral is defined by `5` parameters.

To construct a quadrilateral, 4 sides (`bar(AB)`, `bar(BC)`, `bar(CD)`, `bar(AD)` ) and a diagonal (`bar(AC)`) are given. This is illustrated in the figure. Which of the following helps to construct the specified quadrilateral?

- consider this as two SSS triangles `ABC` and `ACD`
- consider this as two SSS triangles `ABC` and `ACD`
- the quadrilateral cannot be constructed

The answer is "consider this as two SSS triangles `ABC` and `ACD`"

To construct a quadrilateral, 4 (`bar(AB)`, `bar(BC)`, `bar(CD)`, `bar(AD)` ) sides and an angle (`/_B`) are given. This is illustrated in the figure. Which of the following helps to construct the specified quadrilateral?

- consider this as two SSS triangles `ABC` and `ACD`
- consider this as an SAS triangle `ABC` and another SSS triangle `ACD`
- consider this as an SAS triangle `ABC` and another SSS triangle `ACD`

The answer is "consider this as an SAS triangle `ABC` and another SSS triangle `ACD`"

To construct a quadrilateral, `3` (`bar(AB)`, `bar(BC)`, `bar(AD)` ) sides and two diagonals (`bar(AC)`, `bar(BD)`) are given. This is illustrated in the figure. Which of the following helps to construct the specified quadrilateral?

- consider this as two SSS triangles `ABC` and `ABD`
- consider this as two SSS triangles `ABC` and `ABD`
- consider this as an SAS triangle `ABC` and another SSS triangle `ACD`

The answer is "consider this as two SSS triangles `ABC` and `ABD`"

To construct a quadrilateral, `3` sides (`bar(AB)`, `bar(BC)`, `bar(AD)` ) and `2` angles (`/_A`, `/_B`) are given. This is illustrated in the figure. Which of the following helps to construct the specified quadrilateral?

- consider this as two SAS triangles `ABC` and `BAD`
- consider this as two SAS triangles `ABC` and `BAD`
- consider this as an SAS triangle `ABC` and another SSS triangle `ACD`

The answer is "consider this as two SAS triangles `ABC` and `BAD`"

To construct a quadrilateral, `2` sides (`bar(AB)`, `bar(BC)` ) and `3` angles (`/_A`, `/_B`, `/_C`)are given. This is illustrated in the figure. Which of the following helps to construct the specified quadrilateral?

- consider this as two SAS triangles `ABC` and `BAD`
- consider this as an SAS triangle `ABC` and another ASA triangle with angles `/_C` and `/_A`
- consider this as an SAS triangle `ABC` and another ASA triangle with angles `/_C` and `/_A`

The answer is "consider this as an SAS triangle `ABC` and another ASA triangle with two angles `/_C` and `/_A`". Note that `/_\ACD` is formed by angles `/_C` and `/_A`

**Construction of Quadrilateral** : Properties of quadrilaterals

• sum of interior angles `360^@` The formulations of questions

• 4 sides and a diagonal

• 3 sided and 2 diagonals

• 4 sides and an angle

• 3 sides and 2 angles

• 2 sides and 3 angles

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