**Chapter 4 Practical Geometry Exercise 4.3**

Question 1.

Construct the following quadrilaterals:

(i) Quadrilateral MORE

MO = 6 cm, ∠R = 105°, OR = 4.5 cm, ∠M = 60°, ∠O = 105°

(ii) Quadrilateral PLAN

PL = 4 cm, LA = 6.5 cm, ∠P = 90°, ∠A = 110°, ∠N = 85°

(iii) Parallelogram HEAR

HE = 5 cm, EA = 6 cm, ∠R = 85°

(iv) Rectangle OKAY

OK = 7 cm, KA = 5 cm

Solution:

(i) Construction:

Step I: Draw OR = 4.5 cm

Step II: Draw two angles of 105° each at O and R with the help of protactor.

Step III: Cut OM = 6 cm.

Step IV: Draw an angle of 60° at M to meet the angle line through R at E.

Thus, MORE is the required quadrilateral.

(ii) Construction:

Step I: Draw LA = 6.5 cm

Step II: Draw an angle of 75° at L and 110° at A with the help of a protractor.

[∵ 360° – (110° + 90° + 85°) = 75°]

Step III: Cut LP = 4 cm.

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

Thus PLAN is the required quadrilateral.

(iii) Construction: (Opposite sides of a parallelogram are equal)

Step I: Draw HE = 5 cm.

Step II: Draw an angle of 85° at E and cut EA = 6 cm.

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

Step IV: Draw another arc with centre H and radius 6 cm to meet the previous arc at R.

Step V: Join HR and AR

Thus, HEAR is the required parallelogram.

(iv) Construction:

(Each angle of a rectangle is 90° and opposite sides are equal.)

Step I: Draw OK = 7 cm.

Step II: Draw the angle of 90° at K and cut KA = 5 cm.

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

Step IV: Draw another arc with centre A and radius 7 cm to meet the previous arc at Y.

Step V: Join OY and AY.

Thus OKAY is the required rectangle.