RD Sharma solution class 8 chapter 18 Practical Geometry(constructions) Exercise 18.4

Exercise 18.4

Page-18.10

Question 1:

Construct a quadrilateral ABCD, in which AB = 6 cm, BC = 4 cm, CD = 4 cm, ∠B = 95° and ∠C = 90°.

Answer 1:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{BC}=4 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{ABC}=95° \mathrm{at} \mathrm{B}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 6 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{BA}=6 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{Construct} \angle \mathrm{BCD}=90° \mathrm{at} \mathrm{C}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 4 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{BA}=4 \mathrm{cm}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{CD}. \\ \mathrm{The} \mathrm{quadrilateral} \mathrm{so} \mathrm{obtained} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 2:

Construct a quadrilateral ABCD, where AB = 4.2 cm, BC = 3.6 cm, CD = 4.8 cm, ∠B = 30° and ∠C = 150°.

Answer 2:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{BC}=3.6 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{ABC}=30° \mathrm{at} \mathrm{B}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 4.2 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{BA}=4.2 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{Construct} \angle \mathrm{BCD}=150° \mathrm{at} \mathrm{C}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 4.8 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{CD}=4.8 \mathrm{cm}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{AD}. \\ \mathrm{The} \mathrm{quadrilateral} \mathrm{so} \mathrm{obtained} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 3:

Construct a quadrilateral PQRS, in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ∠Q = 75° and ∠R = 120°.

Answer 3:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{QR}=2.5 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{PQR}=75° \mathrm{at} \mathrm{Q}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{Q} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.5 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{QP}=3.5 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{Construct} \angle \mathrm{QRS}=120° \mathrm{at} \mathrm{R}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{R} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 4.1 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{RS}=4.1 \mathrm{cm}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{PS} \\ \mathrm{The} \mathrm{quadrilateral} \mathrm{so} \mathrm{obtained} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Page-18.11

Question 4:

Construct a quadrilateral ABCD given BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 cm and ∠D = 100° and ∠C = 95°.

Answer 4:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{DC}=4.4 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{ADC}=100° \mathrm{at} \mathrm{D}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{D} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 5.6 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{DA}=5.6 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{Construct} \angle \mathrm{BCD}=95° \mathrm{at} \mathrm{C}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 6.6 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{CB}=6.6 \mathrm{cm}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{AB}. \\ \mathrm{The} \mathrm{quadrilateral} \mathrm{so} \mathrm{obtained} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 5:

Construct a quadrilateral ABCD, in which AD = 3.5 cm, AB = 4.4 cm, BC = 4.7 cm, ∠A = 125° and ∠B = 120°.

Answer 5:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AB}=4.4 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{BAD}=125° \mathrm{at} \mathrm{A}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.5 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{AD}=3.5 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{Construct} \angle \mathrm{ABC}=120° \mathrm{at} \mathrm{B}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 4.7 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{BC}=4.7 \mathrm{cm}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{CD}. \\ \mathrm{The} \mathrm{quadrilateral} \mathrm{so} \mathrm{obtained} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 6:

Construct a quadrilateral PQRS, in which ∠Q = 45°, ∠R = 90°, QR = 5 cm, PQ = 9 cm and Rs = 7 cm.

Answer 6:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{QR}=5 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{PQR}=45° \mathrm{at} \mathrm{Q}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{Q} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 9 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{QP}=9 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{Construct} \angle \mathrm{QRS}=90° \mathrm{at} \mathrm{R}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{R} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 7 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{RS}=7 \mathrm{cm}. \\ \mathrm{Since}, \mathrm{the} \mathrm{line} \mathrm{segment} \mathrm{PQ} \mathrm{and} \mathrm{RS} \mathrm{intersect} \mathrm{each} \mathrm{other}, \mathrm{the} \mathrm{quadrilateral} \mathrm{cannot} \mathrm{be} \mathrm{constructed}. \end{gathered}$$

Question 7:

Construct a quadrilateral ABCD, in which AB = BC = 3 cm, AD = 5 cm, ∠A = 90° and ∠B = 105°.

Answer 7:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AB}=3 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{DAB}=90° \mathrm{at} \mathrm{A}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 5 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{AD}=5 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{Construct} \angle \mathrm{ABC}=105° \mathrm{at} \mathrm{B}. \\ \mathrm{Step} V: \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{BC}=3 \mathrm{cm}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{CD}. \\ \mathrm{The} \mathrm{quadrilateral} \mathrm{so} \mathrm{obtained} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 8:

Construct a quadrilateral BDEF, where DE = 4.5 cm, EF = 3.5 cm, FB = 6.5 cm, ∠F = 50° and ∠E = 100°.

Answer 8:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{EF}=3.5 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{DEF}=100° \mathrm{at} \mathrm{E}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{E} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 4.5 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{DE}=4.5 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{Construct} \angle \mathrm{EFB}=50° \mathrm{at} \mathrm{F}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{F} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 6.5 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{FB}=6.5 \mathrm{cm}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{BD}. \\ \mathrm{The} \mathrm{quadrilateral} \mathrm{so} \mathrm{obtained} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$