**Practical Geometry: Construction of Quadrilaterals (Full Chapter) - All Cases**

**Introduction:**
In practical geometry, the construction of quadrilaterals involves drawing four-sided figures using a straightedge and a compass. There are various cases to be considered while constructing quadrilaterals, each with its own set of rules and steps. Let's explore these cases in detail.

**Case 1: Construction of a parallelogram:**
To construct a parallelogram, follow these steps:
1. Draw a line segment AB and extend it.
2. Take a point O on the extended line.
3. With O as the center, draw an arc cutting AB at point C.
4. With C as the center, draw an arc cutting the extended line at point D.
5. Join CD and extend it to meet the extended line segment at point E.
6. Join AE.
7. Thus, AECD forms a parallelogram.

**Case 2: Construction of a rectangle:**
To construct a rectangle, follow these steps:
1. Draw a line segment AB and extend it.
2. Take a point O on the extended line.
3. With O as the center, draw an arc of any radius.
4. With A and B as centers, draw arcs intersecting at point C.
5. Join AC, BC, and CD.
6. Thus, ABCD forms a rectangle.

**Case 3: Construction of a square:**
To construct a square, follow these steps:
1. Draw a line segment AB and extend it.
2. Take a point O on the extended line.
3. With O as the center, draw an arc of any radius.
4. With A and B as centers, draw arcs intersecting at points C and D.
5. Join AC, BC, CD, and DA.
6. Thus, ABCD forms a square.

**Case 4: Construction of a rhombus:**
To construct a rhombus, follow these steps:
1. Draw a line segment AB and extend it.
2. Take a point O on the extended line.
3. With O as the center, draw an arc of any radius.
4. With A and B as centers, draw arcs intersecting at points C and D.
5. Join AC, BC, CD, and DA.
6. Thus, ABCD forms a rhombus.

**Case 5: Construction of a trapezium:**
To construct a trapezium, follow these steps:
1. Draw a line segment AB and extend it.
2. Take a point O on the extended line.
3. With O as the center, draw an arc of any radius.
4. With A and B as centers, draw arcs intersecting at points C and D.
5. Join AC and BD.
6. Thus, ABCD forms a trapezium.

**Case 6: Construction of a kite:**
To construct a kite, follow these steps:
1. Draw a line segment AB and extend it.
2. Take a point O on the extended line.
3. With O as the center, draw an arc of any radius.
4. With A and B as centers, draw arcs intersecting at points C and D.
5. Join AC, CD, and DB.
6. Thus, ABCD forms a kite.

These are the various cases of constructing quadrilaterals. Each case has

A triangle has six elements – 3 sides and 3 angles. To construct a unique triangle, 3 elements out of six elements are required under a certain combination. A quadrilateral has 8 elements 4 sides and 4 angles. In addition to these elements a quadrilateral has 2 diagonals which play an important role in determining the size and shape of a quadrilateral. Thus a quadrilateral has 10 elements (4 sides, 4 angles and 2 diagonals) or measurement

constructing a quadrilateral
To construct a unique quadrilateral we need to know 5 measurements (element) 
note _To construct a unique quadrilateral simply the knowledge of any five elements is not sufficient. We will need to know a combination of specific 5 elements.