Page 195 - ICSE Math 8

5. Is it possible to construct a quadrilateral MASK with MA = 5.1 cm, AS = 7.4 cm, ∠M = 80º,
∠A = 140° and ∠S = 145º? Give reasons for your answer.

Construction of Some Special Quadrilaterals

We can construct some special quadrilaterals (such as square, rectangle, parallelogram, trapezium and rhombus)
using their special properties.
E 6.4 cm B
Example 6: Construct a square CUBE in which CU = 6.4 cm. 90º 90º

Solution: Construction: Draw a rough sketch of the figure to be constructed. 6.4 cm 6.4 cm
Note: In a square, all sides are equal and all angles are equal to 90º. 90º 90º
C 6.4 cm U
Steps of Construction: X Rough sketch Y
E 6.4 cm B
1. Draw line CU = 6.4 cm.
90º 90º
2. At points C and U on line CU, draw –UCX and –CUY
each equal to 90º using a protractor (or compass). 6.4 cm
3. Taking U and C as centres and radius of 6.4 cm, draw 6.4 cm
arcs on line UYCX intersecting them at BE respectively.
Join BE. 90º
Hence, CUBE is the required square. C 6.4 cm U

Example 7: Construct a rectangle DROP in which DR = 6 cm P O
and diagonal DO = 7.4 cm. 7.4 cm
Solution: Construction: Draw a rough sketch of the
figure to be constructed. 90º
Note: In a rectangle, all angles are of 90º D 6 cm R
and opposite sides are equal. Rough sketch
Steps of Construction:

1. Draw a line DR = 6 cm. X Y

2. At points D and R, make –RDX = –DRY = 90º using a P O
protractor (or compass).

3. Taking D as centre and radius = 7.4 cm, draw an arc on line 7.4 cm
RY intersecting it at point O. Join OD.
4. Taking O as centre and radius = 6 cm, draw an arc on 90º
DX intersecting it at P. Join OP. D 6 cm R

Hence, DROP is the required rectangle.

Example 8: Construct a parallelogram MONK in which MO = 5.5 cm, K
ON = 4.5 cm and diagonal MN = 7 cm. 5.5 cm
Solution: Construction: First draw a rough sketch of the figure to be 4.5 cm
constructed. M N
Note: Parallelogram is a quadrilateral in which both pairs of 7 cm
opposite sides are equal. 5.5 cm 4.5 cm
\ KN = MO = 5.5 cm and KM = ON = 4.5 cm O
Rough sketch

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