*NCERT Solutions of Chapter: Practical Geometry. NCERT Solutions along with worksheets and notes for Class 8.*

**Exercise 4.1**

**(1)** **Consider the following quadrilaterals.**

**(i) Quadrilateral ABCD.**

**AB = 4.5 cm**

**BC = 5.5 cm**

**CD = 4cm**

**AD = 6 cm**

**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**

**Ans-**

**(i)**

**Given-**

Quadrilateral ABCD

AB = 4.5 cm

BC = 5.5 cm

CD = 4cm

AD = 6 cm

AC = 7 cm

**Step 1-**

Draw rough sketch of required quadrilateral ABCD.

**Step 2 –**

Draw diagonal AC = 7cm.

**Step 3-**

Draw an arc of 4 cm with C as a center.

**Step 4-**

Draw an arc of 6 cm with A as a center.

**Step 5-**

Mark point of intersection as D and join point D to point A and C.

**Step 6-**

Draw an arc of 5.5cm with C as a centre in other side of the diagonal.

**Step 7-**

Draw an arc of 4.5 cm with A as centre.

**Step 8-**

Mark point of intersection as B. Join point B to point A and C.

We get quadrilateral ABCD.

**(ii)**

**Given-**

Quadrilateral JUMP

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

**Step 1-**

Draw rough sketch of required quadrilateral JUMP.

**Step 2 –**

Draw diagonal PU = 6.5 cm.

**Step 3-**

Draw an arc of 4 cm with U as a center.

**Step 4-**

Draw an arc of 5 cm with P as a center.

**Step 5-**

Mark point of intersection as M and join point M to point P and U.

**Step 6-**

Draw an arc of 3.5 cm with U as a centre in other side of the diagonal.

**Step 7-**

Draw an arc of 4.5 cm with P as centre.

**Step 8-**

Mark point of intersection as J. Join point J to point P and U.

We get required quadrilateral JUMP.

**(iii)**

**Given-**

Parallelogram MORE

OR = 6 cm

RE = 4.5 cm

EO = 7.5 cm

**Ans-**

**Step 1-**

Draw rough sketch of required quadrilateral MORE.

** **

**Step 2 –**

Draw diagonal EO = 7.5 cm.

**Step 3-**

Draw an arc of 4.5 cm with O as a center.

**Step 4-**

Draw an arc of 6 cm with E as a center.

**Step 5-**

Mark point of intersection as M and join point M to point E and O.

**Step 6-**

Draw an arc of 4.5 cm with E as a centre in other side of the diagonal.

**Step 7-**

Draw an arc of 6 cm with O as centre.

**Step 8-**

Mark point of intersection as R. Join point R to point E and O.

We get required parallelogram MORE.

**(iv)**

**Given-**

Rhombus BEST

BE = 4.5 cm

ET = 6 cm

**Ans-**

**Step 1-**

Draw rough sketch of required rhombus BEST.

** **

**Step2 –**

Draw diagonal ET = 6 cm.

**Step 3-**

Draw an arc of 4.5 cm with E as a center.

**Step 4-**

Draw an arc of 4.5 cm with T as a center.

**Step 5-**

Mark point of intersection as B and join point B to point E and T.

**Step 6-**

Draw an arc of 4.5 cm with E as a centre in other side of the diagonal.

**Step 7-**

Draw an arc of 4.5 cm with T as centre.

**Step 8-**

Mark point of intersection as S. Join point S to point E and T.

BEST is required rhombus.

**Step 6- **

Join point B to point E and Point D.

[85° and 110° angles are constructed by protector and ruler. NCERT syllabus is followed.]

[85° and 95° angles are constructed by protector and ruler. NCERT syllabus is followed.]

Note:- No process of drawing 80°, 95°, 100° or any other angle with compass and ruler, which is not in multiple of 15, is explained in NCERT syllabus. Therefore, we are not using any process of construction of these angles with compass. We draw angles which are multiple of 15 with compass and rulers. Any other angles are costructed with help of protactor.

**Helping Topics**