**Geometrical Constructions Class-8 RS** Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-19. We provide step by step Solutions of Exercise / lesson-19 **Geometrical Constructions**** ** for ICSE **Class-8 RS** **Aggarwal** Maths.

Our Solutions contain all type Questions of Exe-19 A, Exe-19 B, with Notes to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-8 Mathematics.

**Geometrical Constructions Class-8 RS** Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-19

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**Notes on Geometrical Constructions**

**Notes on Geometrical Constructions**

Construction” in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil. This is the “pure” form of geometric construction: no numbers involved.

### construction of quadrilaterals

In construction of quadrilaterals we will learn how to construct a quadrilateral. We know that a quadrilateral has ten parts in all: **four sides**, **four angles** and **two diagonals**. To construct a quadrilateral, we shall need data about five specified parts of it.

### Construction of Quadrilaterals

Before talking about the construction of quadrilaterals, let us recall what a quadrilateral is. A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles. The sum of its interior angles is 360 degrees.

A quadrilateral, in general, has sides of different lengths and angles of different measures. However, squares, rectangles, etc. are special types of quadrilaterals with some of their sides and angles being equal. In this article, we will discuss the following construction of quadrilaterals

### Construction of Quadrilaterals when

(i) 4 sides and 1 diagonal is given.

(ii) 3 sides and including 2 angles are given

(iii) 2 sides and three angles are given.

### Tips of Constructions

- Draw rough figure with given measurement
- You should know how to Draw a line bisector , perpendicular bisector and angle bisector
- Idea of constructing angle of 30,45, 60, 75, 90, 105 degree without compass
- Learn the properties of various regular Quadrilaterals
- Then solve example of your text book on
**Geometrical Constructions** - after regular practice you can draw quadrilaterals

** **

**Exe-19 A, Geometrical Constructions Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions**

** Question 1:**

Construct a quadrilateral PQRS in which PQ = 4cm, ∠P = 90**°**, QR = 43 cm, RS = 3.6 cm and SP = 3.2 cm

**Answer** :

**Construction :**

(i) Draw a line segment PQ = 4cm

(ii) At P, draw a ray AX making an angle of 90**°** and cut off PS = 3.2 cm

(iii) With center Q and radius 4.3 cm and with center S and radius 3.6 cm, draw two arcs intersecting each other at R.

(iv) Join RQ and RS

**Then PQRS is the required quadrilateral.**

** **

**Question 2:**

Construct a quadrilateral ABCD in which AB = 4.5 cm, BC = 5.2 cm, CD = 5 cm, DA = 4.7 cm and ∠ABC = 75**°**

**Answer :**

**Construction :**

(i) Draw a line segment AB = 4.5 cm

(ii) At B, draw a ray BX making an angle of 75**°** and cut off BC = 5.2 cm

(iii) With center A and radius 4.7 cm and with center C and radius 5 cm, draw arcs intersecting each other at D.

(iv) Join DA and DC.

**Then ABCD is the required quadrilateral.**

** **

**Question 3:**

Construct a quadrilateral ABCD in which AB = CD= 5.1 cm, BC = 4.7 cm, DA = 4.2 cm and ∠BCD = 60°.

Answer :

**Construction** :

(i) Draw a line segment BC = 4.7 cm

(ii) At C, draw a ray CX making an angle of 60° and cut off CD 5.1 cm.

(iii) With center B and radius 5.1 cm and with center D and radius 4.2 cm, draw arcs intersecting each other at A.

(iv) Join AB and AD

**Then ABCD is the required quadrilateral.**

** **

**Question 4:**

Construct a quadrilateral EFGH in which EF = 6 cm, FG = 5.3 cm, EH = 5 cm, LE = 60° and ∠F = 75°.

**Answer** :

**Construction :**

(i) Draw a line segment EF = 6cm

(ii) At E, draw a ray EX making an angle of 60° and cut off EH = 5 cm.

(iii) At F, draw another ray FY making an angle of 75° and cut off FG = 5.3 cm

(iv) Join HG

**Then EFGIH is the required quadrilateral,**

** **

**Question 5:**

Construct a quadrilateral PORS in which PQ = 4.5 cm, QR = 5.6 Cm, RS = 4.1 cm, ∠Q = 60° and ∠R = 120°.

**Answer** :

**Construction** :

(i) Draw a line segment QR = 4.5 cm

(ii) At Q, draw a ray QX making an angle of 60° and cut off QP = 4.5 cm

(iii) At R, draw a ray RY making an angle of 120° and cut off RS = 4.1 cm

(iv) Join PS

**Then PQRS is the required quadrilateral**

** **

**Question 6:**

Construct a quadrilateral ABCD in which AB = AD = 5.3 cm, BC = CD = 5 cm and diagonal BD = 6.4 cm.

**Answer** :

**Construction:**

(i) Draw line segment BD = 6.4 cm

(ii) With centers B and D, and radius 5.3 cm each draw arcs intersecting each other at

(iii) Join AB and AD

(v) With center B and D and radius 5 cm each draw arcs intersecting each other at C.

(vi) Join BC and DC.

**Then ABCD is the required quadrilateral.**

**Question 7:**

Construct a quadrilateral PQRS in which PQ = 3cm, QR = 2.4 cm, PS = 3.7 cm, PR = 4 cm and QS = 5.5 cm.

**Answer :**

**Construction:**

(i) Draw a line segment PQ = 3cm

(ii) With center P and radius 4 cm and center Q with radius 2.4 cm. Draw arcs interacting each other at R.

(iii) Join PR and QR.

(v) Similarly, with center P and radius 3.7 cm and with center Q and radius 5.5 cm, draw arcs intersecting each other at S.

(v) Join PS and QS

(vi) Join SR.

**Then PQRS is the required quadrilateral.**

**Question 8 :**

Construct a quadrilateral ABCD in which AB = 5.2 cm, BC = 3.6 cm, ∠A = 60°, ∠B 90° and ∠C 120°.

**Answer** :

**Construction:**

(i) Draw a line segment BC = 3.6 cm.

(ii) At B, draw a ray BX making an angle of 90° and cut off BA = 5.2 cm.

(iii) At C, draw a ray CY making an angle of 120°.

(iv) At A, draw another ray AZ making an angle of 60° which intersects CY at D.

**Then ABCD is the required quadrilateral,**

** **

**Question 9 :**

Construct a parallelogram ABCD in which BC = 6cm, CD = 4 cm and ∠C = 60°.

**Answer :**

**Construction :**

(i) Draw line segment BC = 6 cm

(ii) At C, draw a ray CX making an angle of 60° and cut off CD = 4cm

(iii) With center D and radius 6 cm, and with center B and radius 4 cm, draw arc intersecting each other at A.

(iv) Join AB and AD.

**Then ABCD is the required parallelogram.**

** **

**Question 10 :**

Construct a parallelogram PQRS in which QR = 4.7 cm, ∠Q = 120° and PQ = 2.8 cm.

**Answer** :

(i) Draw a line segment QR = 4.7 cm

(ii) ATQ, draw a ray making an angle of 120° and cut off PQ = 2.7 cm.

(iii) With center P and radius 4.7 ad with center R and radius 2.7 cm, draw arcs intersecting each other at S.

(iv) Join SR and SP

(v) Then PORS is the required parallelogram.

Question 11:

Construct a parallelogram ABCD in which BC = 5 cm, CD = 3 cm and diagonal BD = 6cm.

Answer ;

**Construction:**

(i) Draw a line segment BC = 5 cm.

(ii) With center B and radius 6 cm and with center C and radius 5 cm draw arcs which intersect each other at D.

(iii) Join BD and CD.

(iv) Again with center B and radius 3 cm and with center D and radius 5 cm, draw arcs which intersects each other at A.

(v) Join AB and AD

**Then ABCD is the required parallelogram.**

** **

**Question 12:**

Construct a parallelogram ABCD in which AB = 4.8 cm, BC = 3.5 cm and diagonal AC = 5.4 cm.

Answer :

**Construction:**

(i) Draw a line segment AB = 4.8 cm

(ii) With center A and radius 5.4 cm and with center B and radius 3.5 cm, draw arcs which intersect each other at C.

(iii) Join AC and BC

(iv) Again with center A and radius 3.5 cm and with center C and radius 4.8 cm, draw arcs which intersect each other at D.

(v) Join AD and CD,

**Then ABCD is the required parallelogram.**

** **

**Question 13:**

Construct a parallelogram ABCD in which diagonal AC = 5.6 cm and diagonal BD = 6.2 cm and angle between them is 60°.

Answer :

**Construction :**

We know diagonals of a parallelogram bisect each other

AC and BD bisect each other at O

B0 = OD

= 6.2/2 = 3.1 cm

(i) Now draw a line segment AC 5.6 cm

(ii) Bisect each other at O.

(iii) At 0, draw a line making an angle of 60° and produce it to both sides.

(iv) Cut off OB = OD = 6.2/2 = 3.1 cm each

(v) Join AB, BC, CD and DA

**Then ABCD is the required parallelogram.**

** Exe-19 B, Geometrical Constructions Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions**

**Question 1:**

Construct a rectangle whose adjacent sides are 47 cm and 3.2 cm.

**Answer :**

Construction :

(i) Draw line segment AB = 4.7 cm.

(ii) Construct ∠ABX = 90°.

(iii) With B as center and radius 3.2 cm draw an arc, cutting BX at C.

(iv) With C as center and radius 4.7 cm draw an arc.

(v) With A as center and radius32 cm draw another arc, cutting the previous arc at D.

Join AD and DC.

**ABCD is the required rectangle.**

**Question 2:**

Construct a rectangle ABCD in which AB = 4.5 cm and diagonal AC = 6 cm.

**Answer** :

**Construction:**

(i) Draw a line segment AB = 4.5 cm.

(ii) Construct ∠ABX = 90°.

(iii) With A as center and radius 6 cm draw an arc cutting BX at C.

Join AC.

(iv) With A as center and radius BC draw an arc.

(v) With C as Centre and radius = 4.5 cm draw an arc, cutting the previous arc at D.

(vi) Join AD and DC.

**ABCD is the required rectangle.**

**Question 3:**

Construct a rectangle, ABCD in which diagonal AC = 6.3 cm and the angle between the two diagonals is 45°.

**Answer** :

**Construction :**

(i) Draw a line segment AC = 6.3 cm

(ii) Bisect AC at O.

(iii) At O, draw a line making an angle of 45° and produce it to both sides.

(iv) Cut off OB = OD(1/2)AC

**(Diagonal of a rectangle are equal)**

(v) Join AB, BC, CD and DA

**Then ABCD is the required rectangle.**

**Question 4:**

Construct a square of side 4.8 cm.

**Answer :**

**Construction** :

(i) Draw a line segment AB = 4.8 cm

(ii) At A and B, draw perpendiculars AX and BY and cut off from them AD = BC = 4.8 cm

(iii) Join CD

**Then ABCD is the required square.**

**Question 5:**

Construct a square one of whose diagonals is 5.6 clm.

**Answer** :

**Construction :**

(i) Draw a line segment AC = 5.6 cm.

(ii) Draw the perpendicular bisector of AC, meeting AC at O.

(iii) Produce it to XY.

(iv) On OY cut off OB 2.8. On OX, cut off OD = 2.8 cm.

(v) Join AD and CD.

(iv) Join AB and BC.

**ABCD is the required square.**

**Question 6:**

Construct a rhombus ABCD in which AB = 4.3 cm and ZA = 45°.

**Answer** :

**Construction** :

(i) Draw a line segment AB = 4.3 cm.

(ii) Construct ∠BAX = 45°

(iii) On AX set off AD = 4.3 cm.

(iv) With B as center and radius 4-3 cm draw an arc.

(v) With D as center and radius4:3 cm, draw another arc cutting the previous arc at C.

(vi) Join CB and CD.

**ABCD is the required rhombus.**

**Question 7:**

Construct a rhombus ABCD in which AB = 5 cm and diagonal AC = 6.8 cm.

**Answer :**

**Construction:**

(i) Draw a line segment AB 5 cm.

(ii) With A as center and radius =6:8 cm draw an arc.

(iii) With B as center and radius = 5 cm, draw another arc cutting the previous arc at C.

(iv) Join AC and BC.

(v) With A as center and radius 5 cm draw an arc.

(vi) With C as center and radius= 5 cm draw another arc cutting the previous are at D.

(vii) Join DC and DA.

**ABCD is the required rhombus**

**Question 8:**

Construct a rhombus ABCD in which diagonal AC = 5.8 cm and diagonal BD = 6.4 cm.

**Answer :**

**Construction:**

(i) Draw a line segment AC = 58 cm.

(ii) Draw the perpendicular bisector XOY of AC.

(iii) Cut off OB = 1/2, BD = m1/2 x 6.4 = 3.2 cm and on OY and OD = 32 cm on OX.

(iv) Join AB, BC, CD and DA.

**ABCD is the required rhombus.**

–: End of Geometrical Constructions Class-8 RS Aggarwal Solutions :–

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