Gujarat BoardĀ GSEB Textbook Solutions Class 8 Maths Chapter 4 Practical Geometry Ex 4.3 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 8 Maths Chapter 4 Practical Geometry Ex 4.3

Question 1.

Construct the following quadrilaterals:

(i) Quadrilateral

MORE

MO = 6 cm

OR = 4.5 cm

ā M = 60Ā°

ā O = 105Ā°

ā R = 105Ā°

(ii) Quadrilateral

PLAN

PL = 4 cm

LA = 6.5 cm

ā P = 90Ā°

ā A = 110Ā°

ā N = 85Ā°

(iii) Parallelogram

OKAY

HE = 5 cm

EA = 6 cm

ā R = 85Ā°

(iv) Rectangle

HEAR

OK = 7 cm

KA = 5 cm

Solution:

(i) Steps of constructions:

I. Draw a Line segment MO = 6 cm

II. At M, draw \(\overrightarrow { MX } \) , such that ā OMX = 60Ā°

III. At O, draw \(\overrightarrow { OY } \) , such that ā MOY = 105Ā°

IV. From \(\overrightarrow { OY } \) , cut off OR = 4.5 cm

V. At R, draw \(\overrightarrow { RZ } \) , such that ā ORZ = 105Ā°

Let \(\overrightarrow { RZ } \) intersects \(\overrightarrow { MX } \) at E.

Thus, MORE is the required quadrilateral.

(ii) Steps of construction:

I. Draw a line segment AL = 6.5 cm.

II. At A, draw \(\overrightarrow { AX } \) such that ā LAX = 110Ā°

III. At L, draw \(\overrightarrow { LY } \) such that ā ALY = 75Ā°.

Note: ā L = 75Ā° is not given, but we can determine it using angle sum property

āµ Sum of three given angles

= 110Ā° + 90Ā° + 85Ā° = 285Ā°

ā“ The fourth angle ā L = 360Ā° – 285Ā° = 75Ā°

IV. rom \(\overrightarrow { LY } \) , cut-off LP = 4 cm.

V At P, draw \(\overrightarrow { PZ } \) such that ā LPZ = 90Ā°

Let \(\overrightarrow { PZ } \) and \(\overrightarrow { AX } \) intersect at N.

Thus, PLAN is the required quadrilateral.

(iii) Steps of construction:

I. Draw a line segment \(\overrightarrow { HE } \) = 5 cm.

II. At E, draw \(\overrightarrow { EX } \) such that ā HEA = 85Ā°.

III. From \(\overrightarrow { EX } \) , cut-off EA = 6 cm.

IV. With centre at A and radius = 5 cm, draw an arc towards H.

V With centre at H and radius = 6 cm, draw an arc such that it intersects the previous arc at R.

VI. Join RA and RH.

Thus, HEAR is the required parallelogram

(iv) Steps of construction:

I. Draw a line segment Ok = 7 cm

II. draw \(\overrightarrow { OP } \) such that ā KOP = 90Ā°.

III. From \(\overrightarrow { OP } \) , cut-off \(\overrightarrow { OY } \) = 5 cm.

IV. At K, draw \(\overrightarrow { KQ } \) such that ā OKQ = 90Ā°.

V. From \(\overrightarrow { KQ } \) cut-off KA = 5 cm.

VI. Join A and Y.

Thus, OKAY is the required rectangle