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Given two Adjacent Sides and Three Angles

Construct quadrilateral ABCD, given that = 7cm, = 4cm and

We cannot draw this quadrilateral if we do not know . We can find

 

Step :- (1) Draw a the line segment = 7cm. Draw using a protractor


 

(2) With A as centre and radius 4 cm cut an arc on the line.


 

(3) At B draw an angle of .

(4) At D draw an angle of with a protractor. Let the arms of these angles meet at C. ABCD is the required Quadrilateral.


 

Construction :-

rough figure

 

To construct a quadrilateral given three angles and two included sides (ASASA case)
Let the given angles be

A = 75°, C = 85°, D = 68°, and the given sides be AD = 6.1 cm, DC = 7.5 cm.
 

Here also, we can construct the quadrilateral directly, without dividing it into two triangles.

Construct AD = 6.1 cm.

At D, draw ADX = 68°.

With D as centre and radius 7.5 cm cut off

DC = 7.5 cm, on the ray DX.

At A, draw DAY =75°

At C, draw DCZ = 85°.

Let AY and CZ intersect at B.

Then ABCD is the required quadrilateral.

 





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