Many of the things we see in our daily life resemble the mathematical shapes like circle, quadrilateral, triangle etc. The list goes countless as we can’t imagine the world without quadrilaterals. Wherever you see four sides, a quadrilateral is involved there. Let us learn to construct these quadrilaterals. Let’s get right into it.

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## Construction of Quadrilaterals

We can define quadrilaterals as **polygons** that have four sides.

### 1. Construct quadrilaterals when four sides and one diagonal is given.

Construct a quadrilateral PQRS where PQ = 4 cm, Oq = 6 cm, RS = 5 cm, PS = 5.5 cm and PR= 7 cm

- Draw Δ PQR using SSS construction condition.
- With P as the centre, draw an arc of radius 5.5 cm.
- With R as the centre, draw an arc of radius 5 cm.
- S is the point of intersection of the two arcs. Also, mark S and complete PQRS.
- PQRS is the required quadrilateral.

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### 2. Construct quadrilaterals when four sides and one diagonal is given.

Construct a quadrilateral ABCD where BC = 4.5 cm, AD = 5.5 cm, CD = 5cm and the diagonal AC = 5.5 cm, diagonal BD = 7 cm

- Draw ΔACD using SSS construction condition
- Taking D as the centre, draw an arc of radius 7 cm.
- Now let C be the centre, draw an arc of radius 4.5 cm
- Since B lies on both the arcs, B is the point intersection of the two arcs.
- Mark B and complete ABCD.
- ABCD is the required quadrilateral

### 3. Construct quadrilaterals when two adjacent sides and three angles are known.

Construct a qudrilateral PQRS where PQ = 3.5 cm, QR = 6cm, P = 75° , Q= 135° and R = 120°

- Draw PQ = 3.5 cm and construct PQX = 135.
- Cut off QR = 6 cm.
- Make QRY = 120°
- Make QPZ = 75° at M.
- Mark that point, where RY and PZ meet, as S
- We get the required quadrilateral PQRS

### 4. Construct a parallelogram when two consecutive sides and the included angle are given.

Construct a parallelogram ABCD with sides AB = 4 cm and AD = 5 cm and ∠A = 60

- First, construct a line segment
*AB*= 4 cm and construct a 60 angle at point*A*. - Now construct a line segment
*AD*= 5 cm on the other arm of the angle. Then, place the sharp point of the compasses at*B*and make an arc 5 cm above*B*. - Stretch your compasses to 4 cm, place the sharp end at
*D*and draw an arc to intersect the arc drawn in step 2. - Label the intersecting point
*C.*Join*C*to*D*and*B*to*C*to form the parallelogram*ABCD.*

### 5. Construct a parallelogram when two consecutive sides and a diagonal are given.

Construct a parallelogram ABCD in which AB = 6cm, BC = 4.5cm and diagonal AC = 6.8 cm.

- Draw AB = 6 cm.
- With A as centre and radius 6.8 cm, draw an arc.
- With B as centre and radius, 4.5 cm draw another arc, cutting the previous arc at C.
- Join BC and AC.
- With A as centre and radius 4.5 cm, draw an arc.
- With C as centre and radius, 6 cm draw another arc, cutting the previously drawn arc at D.
- Join DA and DC
- ABCD is the required parallelogram.

** **6. When three sides and two included angles are given.

Construct a quadrilateral DEAR, where DE = 4cm, EA = 5cm and AR = 4.5 cm

Given ∠E is = 60° and ∠A = 90°

- Draw a rough sketch of quadrilateral DEAR
- Draw line segment EA = 5 cm and construct the angle of 60 °with the help of a protractor on it. At a distance of 4 cm from E, mark a point D on the angle.
- At point A, construct an angle of 90° with the help of a protractor and at a distance of 4.5 cm and mark a point R on it.
- Join points R and D.
- DEAR is the required quadrilateral.

### 7. Construct a square when one side is given.

- Draw a line segment AB of given length and extend the line AB to the right.
- Set the compass on B with any convenient radius. Draw an arc on each side of B, creating the two points F and G.
- Keeping the compass on G with any convenient radius, draw an arc above the point B.
- Without changing the compass radius, place the compasses on F and draw an arc above B, crossing the previous arc, and creating point H
- Draw a line from B through H.
- Set the compass on A and set its radius to AB. This radius will remains as we create the square’s other three sides.
- Draw an arc above point A.
- Without changing the radius, move the compass to point B. Draw an arc across BH creating point C – a vertex of the square.
- Without changing the radius, move the compasses to C. Draw an arc to the left of C across the existing arc, creating point D – a vertex of the square. Draw the lines CD and AD
- ABCD is a square where each side has a length AB

## Solved Example For You

**Question 1: Which type of quadrilateral is this**

**Rhombus****Rectangle****Kite****Trapezium**

**Answer :** A. AB = BC = CD= AD

AD|| BC, CD||AD

All sides have equal length, opposite sides are parallel and opposite angles are parallel.

**Question 2: What shapes are quadrilaterals?**

Answer: A quadrilateral refers to a four-sided polygon that has four angles. There are many types of quadrilaterals. The five most common types of quadrilaterals are the parallelogram, the rectangle, the square, the trapezoid, and the rhombus.

**Question 3: Is trapezoid a quadrilateral?**

**Answer:** Trapezoids consist of only one pair of parallel sides. On the other hand, parallelograms have two pairs of parallel sides. Thus, a trapezoid can never be a parallelogram. Thus, all trapezoids are quadrilaterals. They are four-sided polygons, thus it makes them quadrilaterals.

**Question 4: How many quadrilaterals are there?**

**Answer:** A quadrilateral is basically a polygon that has four sides. There are seven quadrilaterals, both familiar and not so familiar. They are kite, parallelogram, rhombus, rectangle, square, trapezoid, and isosceles trapezoid.

**Question 5: Who invented quadrilateral?**

**Answer:** It is said that the Ancient Greeks invented the quadrilateral. We also study that Pythagoras was the first to draw one. Moreover, back in those days, quadrilaterals consisted of three sides and their properties were merely faintly understood

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