Q. 2

Construct quadrilaterals with the measurements given below:

Parallelogram GRAM with GR = AM = 5 cm, RA = MG = 6.2 cm and R = 85o.

Answer :

GIVEN : In Parallelogram GRAM,


GR = AM = 5 cm


RA = MG = 6.2 cm


R = 85o


PROCEDURE :


Step 1 : draw a rough sketch of the parallelogram GRAM and mark the given measurements.


Since the given measurements are not sufficient for construction , we shall find the required measurements using the properties of the parallelogram.


As opposite angles of parallelogram are equal so , R = M = 85o and as the consecutive angles are supplementary so , G = 180° - 85° = 95°.


Thus G = A = 95°.



Step 2 : construct ΔGRA using SAS property of construction model with GR = 5cm , R = 85o and RA = 6.2 cm.



Step 3 : construct G = 95° and draw GY || RA.



Step 4 : construct A = 95° and draw AN to meet GY at M.


GRAM is the required quadrilateral (ie. Parallelogram).



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