Practical Geometry - Exercise 4.1 - NCERT Solutions

Chapter 4 PRACTICAL GEOMETRY

Exercise 4.1

Q.1 Construct the following quadrilaterals.

(i) Quadrilateral ABCD.

AB = 4.5 cm

BC = 5.5 cm

CD = 4 cm

AD = 6 cm

AC = 7 cm

Sol. Step 1: Construct ΔABC using SSS criterion.

Step 2: Keep A as centre and draw an arc of radius 6 cm on the opposite side of point B.

Step 3: Draw an another arc keeping centre as C of radius 4 cm, such that it intersects the arc drawn in the above step. The intersecting point of both the arcs will be point D.

To complete the quadrilateral ABCD, join points A and C to D.

(ii) Quadrilateral JUMP

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

Sol. Step 1: Construct ΔJUP using SSS criterion.

Step 2: Keep P as centre and draw an arc of radius 5 cm on the opposite side of point J. Draw an another arc keeping centre as U of radius 4 cm, such that it intersects the previous drawn arc. Let the point of intersection be M.

Step 3: To complete the quadrilateral JUMP, join points P and U to M.

(iii) Parallelogram MORE

OR = 6 cm

RE = 4.5 cm

EO = 7.5 cm

Sol. Step 1: Construct ΔEOR using SSS criterion

Step 2: Take O and E as centres with arcs of radius 4.5 cm and 6 cm. These two arcs must intersect and this is the point M.

Step 3: To complete the parallelogram MORE, join O and E to M.

(iv) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

Sol. Step 1: Construct ΔBET using SSS criterion

Step 2: Keep E as centre and draw an arc of radius 4.5 cm on the opposite side of point B. Draw an another arc keeping centre as T of radius 4.5 cm, such that it intersects the previous drawn arc. Let the point of intersection be S.

Step 3: To complete the parallelogram BEST, join E and T to S.