Construct the following quadrilaterals:

(i) Quadrilateral MORE

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

Solution:

Construction steps:

Step I: Draw a line segment OR = 4.5 cm

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

Step III: Cut OM = 6 cm.

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

Hence, MORE is the required quadrilateral.

(ii) Quadrilateral PLAN

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

Solution:

Construction steps:

Step I: Draw a line segment LA = 6.5 cm

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

Thus,

[∵ 360° – (110° + 90° + 85°) = 75°]

Now,

Step III: Cut LP = 4 cm.

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

Hence, PLAN is the required quadrilateral.

(iii) Parallelogram HEAR

HE = 5 cm, EA = 6 cm, ∠R = 85°

Solution:

Construction steps:

(We know that opposite sides of a parallelogram are equal)

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

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

Step III: With centre A draw an arc of radius 5 cm.

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

Step V: Join HR and AR

Hence, HEAR is the required parallelogram.

(iv) Rectangle OKAY

OK = 7 cm, KA = 5 cm

Solution:

Construction steps:

(We know that each angle of a rectangle is 90° and opposite sides are equal.)

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

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

Step III: With centre O draw an arc of 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.

Hence, OKAY is the required rectangle.