Q. 2

# Construct quadrilaterals with the measurements given below:

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

Answer :

GIVEN : In Parallelogram GRAM,

GR = AM = 5 cm

RA = MG = 6.2 cm

∠R = 85^{o}

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 = 85^{o} 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 = 85^{o} 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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