1.Construct the following quadrilaterals:

(i) Quadrilateral MORE

MO = 6 cm ∠R = \(105^{\circ}\), OR = 4.5 cm, ∠M = \(60^{\circ}\), ∠O = \(105^{\circ}\)

(ii) Quadrilateral PLAN

PL = 4 cm, LA = 6.5 cm, ∠P = \(90^{\circ}\), ∠A = \(110^{\circ}\), ∠N = \(85^{\circ}\)

(iii) Parallelogram HEAR

HE = 5 cm, EA = 6 cm, ∠R = \(85^{\circ}\)

(iv) Rectangle OKAY

OK = 7 cm, KA = 5 cm

(i) Draw a rough sketch first as per the given dimensions.


Construction:

Step 1: Draw a line segment OR = 4.5 cm

Step 2: Draw an angle of \(105^{\circ}\) at O and also an angle of \(105^{\circ}\) at R with the help of protractor.

Step 3: Make an arc OM = 6 cm.

Step 4: Draw an angle of \(60^{\circ}\) at M to meet the line through R at E.

Hence we have, MORE as the required quadrilateral.

(ii)Draw a rough sketch first as per the given dimensions.


Construction:

Step 1: Draw a line segment LA = 6.5 cm

Step 2: Draw an angle of 75° at L and \(110^{\circ}\) at A with the help of a protractor. [\(∵ 360^{\circ} – (110^{\circ} + 90^{\circ} + 85^{\circ}) = 75^{\circ}\)]

Step 3: Cut LP = 4 cm.

Step 4: Draw an angle of 90° at P which meets the line through A at N.

Hence we have PLAN as the required quadrilateral.

(iii)Draw a rough sketch first as per the given dimensions and we know that opposite sides of a parallelogram are equal.


Construction:

Step 1: Draw a line segment HE = 5 cm.

Step 2: Draw an angle of \(85^{\circ}\) at E and cut an arc of EA = 6 cm.

Step 3: Draw an arc with centre A and radius 5 cm.

Step 4: Draw another arc with centre H and radius 6 cm to meet the previous arc at R and join HR and AR.

Hence we have, HEAR as the required parallelogram.

(iv)Draw a rough sketch first as per the given dimensions and we know that each angle of a rectangle is \(90^{\circ}\) and opposite sides are equal.


Construction:

Step 1: Draw a line segment OK = 7 cm.

Step 2: Draw the angle of \(90^{\circ}\) at K and cut an arc of KA = 5 cm.

Step 3: Draw an arc with centre at O and radius 5 cm.

Step 4: Draw another arc with centre at A and radius 7 cm to meet the previous arc at Y and join OY and AY.

Hence we have OKAY as the required rectangle.