# 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 Î”ABC 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 Î”JUP 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 Î”EOR 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 Î”BET 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.