NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.2 – Practical Geometry, has been designed by the NCERT to test the knowledge of the student on the topic – Constructing a Quadrilateral – When two diagonals and three sides are given

### NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.2 – Practical Geometry

**NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.2 – Practical Geometry**

**1. Construct the following quadrilaterals**

**i. Quadrilateral LIFT**

**LI = 4 cm IF = 3 cm TL = 2.5 cm LF = 4.5 cm IT = 4 cm**

**Solution:**

**Steps of construction**

- Step 1. Draw the side LI = 4 cm
- Step 2. With L as centre and radius 2.5 cm (= LT), draw an arc on one side of LI
- Step 3. With I as centre and radius 4 cm (= IT), draw an arc intersecting the previous arc at point T
- Step 4. With L as centre and radius 4.5 cm (= LF), draw an arc on same side of LI
- Step 5. With I as centre and radius 3 cm (= IF), draw an arc intersecting the previous arc at point F
- Step 6. Join LT, TF and FI

LIFT is the required quadrilateral.

**ii. Quadrilateral GOLD**

**OL = 7.5 cm **

**GL = 6 cm**

**GD = 6 cm**

**LD = 6 cm**

**OD = 10 cm**

**Solution:**

**Steps of construction**

- Step 1. Draw the side LD = 6 cm
- Step 2. With L as centre and radius 6 cm (= GL), draw an arc on one side of LD
- Step 3. With D as centre and radius 6 cm (= GD), draw an arc intersecting the previous arc at point G
- Step 4. With L as centre and radius 7.5 cm (= OL), draw an arc on same side of LD
- Step 5. With D as centre and radius 10 cm (= OD), draw an arc intersecting the previous arc at point O
- Step 6. Join GD, OG and OL

GOLD is the required quadrilateral.

**iii. Rhombus BEND**

**BN = 5.6 cm **

**DE = 6.5 cm**

**Solution:**

**Steps of construction**

- Step 1. Draw the diagonal DE = 6.5 cm
- Step 2. Draw a perpendicular bisector of DE intersecting it at O
- Step 3. With O as centre and radius 2.8 cm (= ), draw an arc intersecting the perpendicular bisector at B and N
- Step 4. Join BE, EN, ND and DB

BEND is the required rhombus.

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