# How to draw a parallelogram ,rhombus ,trapezium

Dear student,

1.
A parallelogram can be constructed in several ways.
Following are the steps of construction of a parallelogram whose two sides are 7cm and 5 cm respectively and ∠A = 45°.

(i) Construct line segment AB of length 7 cm.

(ii) At point A, construct angle of 45° with the help of compass and name it as ∠BAL.

(iii) Taking 5 cm as radius, mark an arc on the ray AL and name the point of intersection as D.

(iv) From point B, construct ray BK parallel to AD.

(v) Taking 5 cm as radius, mark an arc on ray BK and name it as C.

(vi) Join CD. ABCD is the required parallelogram.

2. For Rhombus:

Same steps are to be followed as above but taking the same length of sides.

3. Trapezium:

We can understand that by taking an example : construct a trapezium ABCD in AB | | DC , AB = 6 c m , DC = 3.5 c m , angle A = 55° and AD = 3.2 cm

Solution  : we follow these steps to construct required t​rapezium ABCD , from given information , As :

Step 1 : Draw a line AB  =  6 cm

Step 2 : Draw 55$°$ at point A , with the help of protractor.  we get $\angle$ BAX  =  55​$°$ .

Step 3 : Take radius of 3.2 cm and center " A " draw an arc that intersect line AX at " D " .

We know in trapezium adjacent angles are supplementary  ,  So ​$\angle$ A + ​$\angle$ D  =  180​$°$
So,

55​$°$ + ​​$\angle$ D  =  180​$°$

$\angle$ D  =  125​$°$

Step 4 : Draw 125​​​$°$ at point " D " with the help of protractor.   we get ​$\angle$ ADY  =  125$°$

Step 5 : Take radius of 3.5 cm and center " D " draw an arc that intersect line DY at  " C " .

Step 6 : Join CB , we get required trapezium ABCD .

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Regards.

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