## MP Board Class 8th Maths Solutions Chapter 4 Practical Geometry Ex 4.3

Question 1.

Construct the following quadrilaterals.

(i) Quadrilateral

MORE

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 1050°

∠R = 105°

(ii) Quadrilateral

PLAN

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 6.5 cm

∠N = 85°

(iii) Parallelogram

HEAR

HE =5 cm

EA = 6 cm

∠B = 85°

(iv) Rectangle

OKAY

OK = 7 cm

KA = 5 cm

Solution:

(i) Steps of Construction:

Step-1: Draw MO = 6 cm

Step-2 : Make ∠MOX = 105° and ∠OMY = 60°.

Step-3 : Cut off OR = 4.5 cm on OX.

Step-4 : At point R, draw ∠ORZ = 105° which cuts MY at E.

Hence, MORE is the required quadrilateral.

(ii) Here, ∠P = 90°, ∠A = 110°, ∠N = 85°

∴ ∠L = 360° – (∠P + ∠A + ∠N)

= 360° – (90° + 110° + 85°)

= 360°- 285° = 75° ….. (A)

Steps of Construction:

Step-1: Draw PL = 4 cm.

Step-2 : Make ∠LPX = 90° and ∠PLY = 75°. [From (A)]

Step-3 : Cut off LA = 6.5 cm on \(\overrightarrow{L Y}\).

Step-4: Draw ∠LAZ = 110° which cut \(\overrightarrow{P X}\) at point N.

Hence, PLAN is the required quadrilateral.

(iii) Since, opposite sides and angles of a parallelogram are equal i.e., ∠R = ∠E = 85°, HE = RA = 5 cm and EA = HR = 6 cm.

Steps of Construction:

Step-1: Draw HE = 5 cm.

Step-2 : Draw ∠HEX = 85°.

Step-3 : Cut off EA = 6 cm on \(\overrightarrow{E X}\)

Step-4: With H as centre and radius equal to 6 cm, draw an arc.

Step-5: With A as centre and radius equal to 5 cm, cut another arc on the arc drawn in step-4 at point R.

Step-6 : Join HR and RA.

Hence HEAR is the required parallelogram.

(iv) We know that each of the four angles of a rectangle is equal to 90° and opposite sides are also equal.

OK = YA and KA = OY

Steps of Construction:

Step-1: Draw OK = 7 cm.

Step-2 : Make ∠OKX = 90°.

Step-3 : Cut off KA = 5 cm on \(\overrightarrow{K X}\).

Step-4: With O as centre and radius equal to 5 cm, cut an arc.

Step-5: With A as centre and radius equal to 7 cm cut another arc on the arc drawn in step-4 at point Y.

Step-6 : Join OY and YA.

Hence, OKAY is the required rectangle.