Q. 34.8( 12 Votes )

# Construct the quadrilaterals with the given measurements. And write steps of construction.

Parallelogram PQRS with PQ = 4.5 cm, QR = 3 cm and ∠PQR = 60^{o}.

Answer :

GIVEN : In Parallelogram PQRS,

PQ = 4.5 cm

QR = 3 cm

∠PQR = 60^{o}

PROCEDURE :

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

Here , we are given only 3 measurements. But as PQRS is a parallelogram , we can also write that RS = PQ = 4.5 cm and SP = QR = 3 cm.

(now we got 5 measurements in total)

Step 2 : Draw ΔPQR using the measures PQ = 4.5 cm , ∠PQR = 60°

and QR = 3 cm.

Step 3 : Locate the 4^{th} vertex ‘S’ using the other 2 measurements PS = 3 cm and RS = 4.5 cm. To locate the fourth vertex ‘S’ , draw an arc , with center P and radius 3cm (PS=3cm).

Draw another arc with center R and radius 4.5cm (RS=4.5cm) which cuts the previous arc at S.

Step 4 : Join RS and PS to complete the required parallelogram.

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