Constructing a Quadrilateral

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Slide 1

Constructing a Quadrilateral

Slide 2

We shall learn how to construct a unique quadrilateral by following methods :-

When four sides and one diagonal are given.

When two diagonals and three sides are given.

When two adjacent sides and three angles are given.

When three sides and two included angles are given.

When other special properties are known.

Slide 3

Constructing a quadrilateral when four sides and one diagonal are given

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

7 cm

4 cm

6 cm

5.5 cm

5 cm

S

R

Q

P

ROUGH SKETCH

Slide 4

4 cm

6 cm

R

P Step 1 :- Construct a triangle PQR using SSS criterion.

7 cm

Q

Slide 5

Step 2 :- With P as centre draw an arc of radius 5.5 cm .

4 cm

6 cm

R

P

7 cm

Q

Slide 6

Step 3 :- Now, with R as centre draw an arc of radius 5 cm intersecting another arc at point S

4 cm

6 cm

R

P

7 cm

Q

S

Slide 7

Step 4 :- Now join PS and RS.

PQRS is the required quadrilateral.

4 cm

6 cm

S

P

7 cm

Q

R

Slide 8

Constructing a quadrilateral when two diagonals and three sides are given.

Example : Construct a quadrilateral ABCD, given that BC =4.5 cm, AD = 5.5 cm, CD = 5 cm, AC = 5.5 cm and diagonal BD = 7 cm.

ROUGH SKETCH

C

D

A

B

7 cm

5 cm

5.5 cm

5.5cm

4.5 cm

Slide 9

Step 1 :- Draw triangle ACD using SSS criterion

C

D

A

5.5 cm

5 cm

5.5 cm

Slide 10

Step 2 :- With D as centre draw an arc of radius 7 cm.

C

D

A

5.5 cm

5 cm

5.5 cm

Slide 11

Step 3 :- Now, with C as centre draw an arc of radius 4.5 cm intersecting another arc at point B.

C

D

A

5.5 cm

5 cm

5.5 cm

B

Slide 12