Question

Construct a parallelogram PQRS with
PQ = 6 cm, PS = 5.3 cm and angle P = 120°.​

Answer 1

Answer:

★ Steps to construct a paralleogram:-

$\underline{\underline{\rm\blue{Step \: 1:-}}}$

Draw a line segment PQ = 6 cm

$\underline{\underline{\rm\blue{Step \: 2:-}}}$

Using a compass and taking P as centre construct an angle of 120°.

$\underline{\underline{\rm\blue{Step \: 3:-}}}$

Take radius of 5.3 cm, and draw an arc on 120° angle line. This will be the point S

$\underline{\underline{\rm\blue{Step \: 4:-}}}$

According to the supplementary property of a parallelogram, SPQ + PQR = 180. Hence draw an angle of 60° on point Q.

$\underline{\underline{\rm\blue{Step \: 5:-}}}$

Draw a line segment from S. The point where the line segment of angle 60° will intersect will be R.

$\underline{\underline{\rm\blue{Step \: 6:-}}}$

Join PQRS to form a parallelogram.

★ Construction:-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf P}\qbezier(1,1)(1,1)(0,4)\put(6.2,0.5){\bf Q}\qbezier(0,4)(0,4)(5,4)\put( - 0.5,4){\bf S}\qbezier(6,1)(6,1)(5,4)\put(5.5,3.8){\bf R}\put(3,0.5){\bf 6 cm}\put(5.5,3.8){\bf R}\put( - 0.7,2){\bf 5.3 cm}\qbezier(1.5,1)(1.4,1.6)(0.9,1.5)\put(1.4,1.5){\bf 120^ \circ }\end{picture}$

Answer 2

-

★ Steps to construct a paralleogram :-

Draw a line segment PQ = 6 cm

Using a compass and taking P as centre construct an angle of 120°.

Take radius of 5.3 cm, and draw an arc on 120° angle line. This will be the point S.

According to the supplementary property of a parallelogram, SPQ + PQR = 180. Hence draw an angle of 60° on point Q.

Draw a line segment from S. The point where the line segment of angle 60° will intersect will be R.

Join PQRS to form a parallelogram.

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★ Construction :-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf P}\qbezier(1,1)(1,1)(0,4)\put(6.2,0.5){\bf Q}\qbezier(0,4)(0,4)(5,4)\put( - 0.5,4){\bf S}\qbezier(6,1)(6,1)(5,4)\put(5.5,3.8){\bf R}\put(3,0.5){\bf 6 cm}\put(5.5,3.8){\bf R}\put( - 0.7,2){\bf 5.3 cm}\qbezier(1.5,1)(1.4,1.6)(0.9,1.5)\put(1.4,1.5){\bf 120^ \circ }\end{picture}$

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