## MP Board Class 8th Maths Solutions Chapter 4 Practical Geometry Ex 4.1

Question 1.

Construct the following quadrilaterals.

(i) Quadrilateral

ABCD

AB = 4.5 cm

BC= 5.5 cm

MP= 5 cm

AD = 6cm

AC = 7 cm

(ii) Quadrilateral

JUMP

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

(iii) Parallelogram

MORE

OR = 6 cm

RE = 4.5 cm

EO = 7.5 cm

(iv) Rhombus

BEST

BE = 4.5 cm

ET = 6 cm

Solution:

(i) Steps of Construction :

Step-1: Draw AB = 4.5 cm.

Step-2: With B as centre and radius equal to 5.5 cm, cut an arc.

Step-3 : With A as centre and radius equal to 7 cm, cut another arc on the arc drawn in step-2 at point C.

Step-4 : With C as centre and radius equal to 4 cm, cut off an arc. Also, with A as centre and. radius equal to 6 cm cut off another arc on the arc just drawn at point D.

Step-5 : Join BC, AC, CD and AD.

Hence, ABCD is the required quadrilateral.

(ii) Steps of Construction :

Step-1: Draw JU = 3.5 cm.

Step-2: With J as centre and radius equal to 4.5 cm, cut an arc.

Step-3 : With U as centre and radius equal to 6.5 cm, cut another arc on the arc drawn in step-2 at point P.

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

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

Step-6 : Join JP, UP, UM and PM. Thus, JUMP is the required quadrilateral.

(iii) We know that opposite sides of a parallelogram are equal and parallel to each other.

∴ OR = ME and MO = ER.

Steps of Construction:

Step-1: Draw OR = 6 cm.

Step-2 : With R as centre and radius equal to 4.5 cm, cut an arc.

Step-3 : With O as centre and radius equal to 7.5 cm, cut another arc on the arc drawn in step-2 at point E.

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

Step-5 : With O as centre and radius equal to 4.5 cm, cut an arc on the arc drawn in step-4 at point M.

Step-6 : Join RE, OE, OM and ME.

Hence, MORE is the required parallelogram.

(iv) We know that all four sides of a rhombus are equal.

∴ BE = ES = ST = BT = 4.5 cm.

Steps of Construction:

Step-1: Draw BE = 4.5 cm.

Step-2: With B as centre and radius equal to 4.5 cm, draw an arc.

Step-3: With E as centre and radius equal to 6 cm, draw another arc, cutting the previous arc at point T.

Step-4: With E as centre and radius equal to 4.5 cm, cut an arc.

Step-5: With T as centre and radius equal to 4.5 cm, cut another arc on the previous arc at point S.

Step-6 : Join BT, ES, ET and ST.

Hence, BEST is the required rhombus.