Construction

Quadrilateral

A quadrilateral is a polygon with four sides (edges), four vertices (corners), and four angles. The sum of the interior angles of any quadrilateral is always 360°.

Parallelogram

A parallelogram is a special type of quadrilateral in which both pairs of opposite sides are parallel and equal in length. The opposite angles are also equal, and the diagonals bisect each other.

✅ Every parallelogram is a quadrilateral, but not every quadrilateral is a parallelogram.

1. Construction of Parallelograms equal in area

- Parallelograms on the same base and between the same parallels are equal in area.

2. Construction of Triangles equal in area

- Triangles on the same base and between the same parallels are equal in area.

3. Construction of Triangles and Parallelograms equal in area

- Triangle with double the base of parallelogram on the same base and between the same parallels are equal in area.

Key Points

1. The naming of the figure must be the same as the question.
2. You must have a rough sketch with proper naming and measurement before working on construction.
3. It is not necessary to mention the working steps.
4. After the construction, you must check it experimentally and theoretically.
5. In the end, the name of the final figure, like \(\triangle ABC\), which was newly constructed, must be mentioned.

Practice questions Construction SEE

Model 1: Construction of a triangle whose area is equal to the area of the given quadrilateral.

1. (a) Construct a quadrilateral ABCD in which AB=BC=6 cm, AD=CD=5.1 cm, and \(\angle DAB = 60^0\). Also, construct a triangle ADM whose area is equal to the area of the quadrilateral. [3A][NEB Model 2080 A]

(b) Are BD || MC? Give a reason. [1HA]

2. (a) Construct a quadrilateral ABCD in which AB=4.5 cm, AC=CD=5 cm, AD = 6 cm and \(\angle BAC = 60^0\). Also, construct a triangle PBC whose area is equal to the area of the quadrilateral ABCD. [3A][NEB Model 2080 B]

(b) Give the reason why the area of the quadrilateral ABCD and the triangle PBC is equal. [1HA]

3.  In quadrilateral ABCD AB = 4.2 cm, BC = 5.6 cm CD = 5 cm DA = 4.8 cm and BD = 6.5 cm. [SEE 2080 LP]

(a) Construct the quadrilateral ABCD according to the above measurements and then construct a triangle that is equal to the quadrilateral in area. [3A]

(b) Why are the areas of the triangle and the quadrilateral so formed equal? Give reason.. [1HA]