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Construction in geometry means to draw shapes, angles or lines accurately. Drawing of geometric items such as lines and circles using only compasses and straight edge.
These constructions use only compass, straightedge (i.e. ruler) and a pencil.
When two adjacent sides are given.
Example:
Construct a rectangle ABCD in which AB = 6cm and BC = 4.5cm.
Steps of Construction:
Thus, ABCD is the required rectangle.
When one side is given
Example:
Construct the square in which AB=5.5cm
Steps of construction;
Thus, ABCD is the required square.
When two adjacent sides and the included angle are given.
Example:
Construct a parallelogram ABCD in which BC = 5.3 cm, CD = 4.6 cm and∠C = 60°.
Steps of Construction:
Thus, ABCD is the required parallelogram.
When one side and one angle are given.
Example:
Construct a rhombus in which AB = 5.5 cm and∠A =45°
Steps of construction:
In a regular pentagon, all sides are equal in length and each interior angle is 108°.In the figure, ABCDE is a regular pentagon.
Example:
Construct a regular pentagon ABCDE in which AB = 3cm.
Steps of construction:
Thus, ABCDE is the required regular pentagon.
In the regular hexagon, all sides are equal in length and each interior angle is 120°.
Also, exterior angle =\(\frac{360°}{n}\)
= \(\frac{360°}{6}\) = 60°
Example:
Construct a regular hexagon ABCDEF in which AB=4cm
Steps of Construction:
Thus, ABCDEF is required regular hexagon.
In a regular octagon, all sides are equal in length and each interior angle is 135°
Example:
Construct a regular octagon having a side 5 cm
Steps of construction:
Solution:
Steps of construction:-
(i) Draw AB = 4.8cm
(ii) At B, construct \(\angle\)PBA=90^{o}
(iii) Taking A as centre, draw an arc of radius 6.2cm which cuts BP at the point C
(iv) Taking C as centre, draw an arc of radius 4.8 cm and taking A as centre draw another arc of radius equal to BC to cut the previous arc at the point D
(v) Join AD and CD
Thus, ABCD is the required rectangle.
Solution:
Steps of construction:
(i) Draw a straight line PR=7 cm
(ii) Find the midpoint O of PR.
(iii) Using a compass, draw a line XY at 45^{o}.
(iv) With the length of OP cut arc
(v) Using scale join PQRS.
(vi) The required figure PQRS is completed.
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