3 Tutor System
Starting just at 265/hour

# 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.