# NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

**NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry- ** In class VII you have already learned how to draw triangles. To draw a unique triangle you require three measurements of sides and angles. In this chapter, you will learn some advanced-level constructions like- quadrilaterals. In this, you are going to learn how to construct a unique quadrilateral when different conditions are given like when the lengths of four sides with a diagonal are given, when three sides and two diagonals are given, when two adjacent sides with three angles are given, etc. Geometry is a subset of Mathematics in which you learn about the shape, size & relative position of geometric figures like- Angle, triangles, rectangles and etc. You know in order to draw a triangle, you need the measurement of three straight lines likewise you can say that the measurement of four lines will help us in creating a rectangle.

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In this chapter, there are a total of 4 exercises and 33 questions. Students must complete the NCERT Class 8 Maths Syllabus as soon as possible. They must also read the NCERT Class 8 Maths Books and complete all the topics. Along with all these, NCERT Solutions for other classes and subjects can be downloaded using the link.

**NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Chapter: Introduction **

**Answer: **No, he cannot construct a unique quadrilateral. The given measurements consist of 2 adjacent sides, the angle between these sides and 2 diagonals. It is not one of the specific combinations to construct a quadrilateral.

Moreover, on trying to construct using these, we find that the vertex C is not fixed and can be varied. Hence, the quadrilateral is not unique.

**NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Excercise: Constructing A Quadrilateral**

**Q (i) ** We saw that 5 measurements of a quadrilateral can determine a quadrilateral uniquely. Do you think any five measurements of the quadrilateral can do this**Answer: **No, any five measurements of the quadrilateral cannot determine a quadrilateral uniquely. For example, consider a quadrilateral ABCD where AB, BC, CD are known and A and C are known. But this cannot uniquely determine the quadrilateral.

**Q (ii) ** Can you draw a parallelogram BATS where BA = 5 cm, AT = 6 cm and

AS = 6.5 cm? Why?

**Answer:**Yes, we can draw a parallelogram BATS where BA = 5 cm, AT = 6 cm and

AS = 6.5 cm (diagonal). We know, diagonals of a parallelogram are equal. Hence, BT = AS =6.5 cm

**Answer:**Yes, we can draw a rhombus ZEAL where ZE = 3.5 cm, diagonal EL = 5 cm.

**Q (iv)**A student attempted to draw a quadrilateral PLAY where and , but could not draw it. What is the reason?

[Hint: Discuss it using a rough sketch].

**Answer:**Given, a quadrilateral PLAY where and ,

Rough sketch:

We know, that sum of two sides of a triangle must be greater than the third side. But PL + PY < YL . Hence this is not a triangle. Therefore, this quadrilateral cannot be made.

**NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise: 4.1 **

**Q1 (i)**Construct the following quadrilaterals

AB = 4.5 cm

BC = 5.5 cm

CD = 4 cm

AD = 6 cm

AC = 7 cm

**Answer:**Given,

AB = 4.5 cm

BC = 5.5 cm

CD = 4 cm

AD = 6 cm

AC = 7 cm

Step 1. Using SSS condition ,draw

Step 2. Now, CD= 4 cm. Using C as centre, draw an arc of radius = 4 cm

Step 3. Also, AD = 6 cm. Using A as centre, draw an arc of radius = 6 cm.

Step 4. Point D will be the point of intersection of the two drawn arcs. Join AD and CD to complete the quadrilateral.

ABCD is the required quadrilateral.

**Q1 (ii) ** Construct the following quadrilaterals.

Quadrilateral JUMP

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

**Answer: **Given,

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

Step 1. Using SSS condition ,draw

Step 2. Now, PM = MP = 5 cm. Using P as centre, draw an arc of radius = 5 cm

Step 3. Also, UM = 4 cm. Using U as centre, draw an arc of radius = 4 cm.

Step 4. Point M will be the point of intersection of the two drawn arcs. Join PM and UM to complete the quadrilateral.

JUMP is the required quadrilateral.

**Q1 (iii) ** Construct the following quadrilaterals.

Parallelogram MORE

OR = 6 cm

RE = 4.5 cm

EO = 7.5 cm

**Answer: **Given,

Parallelogram MORE

OR = 6 cm

RE = 4.5 cm

EO = 7.5 cm

We know, Opposite sides of a parallelogram are equal in length and also parallel to each other

Therefore,

EM = OR = 6 cm,

OM = RE = 4.5 cm

Step 1. Using SSS condition ,draw

Step 2. Now, EM = OR = 6cm . Using E as centre, draw an arc of radius = 6 cm

Step 3. Also, OM = RE = 4.5 cm . Using O as centre, draw an arc of radius = 4.5 cm.

Step 4. Point M will be the point of intersection of the two drawn arcs. Join OM and EM to complete the parallelogram.

MORE is the required parallelogram.

BE = 4.5 cm

ET = 6 cm

**Answer:**Given,

BEST is a rhombus where:

BE = 4.5 cm

ET = 6 cm (diagonal)

We know that the sides of a rhombus are equal in length and opposite sides are parallel to each other.

Therefore, the sides of Rohmbus BE = ES = ST = TB = 4.5 cm

Step 1. Using SSS condition ,draw

Step 2. Now, ES = 4.5 cm . Using E as centre, draw an arc of radius = 4.5 cm

Step 3. Also, TS = 4.5 cm . Using T as centre, draw an arc of radius = 4.5 cm.

Step 4. Point S will be the point of intersection of the two drawn arcs. Join ES and TS to complete the rhombus.

BEST is the required rhombus.

** NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Topic: When Two Diagonals And Three Sides Are Given **

** Answer: **No, it is not possible. We cannot draw ABD first, because neither SSS nor SAS condition is there.

** Answer: **Yes, we can construct a quadrilateral with the given conditions. Here, two diagonals and three sides are given.

(Hint: Construct using SSS condition. Next, find point Q by drawing arcs from P and R. PQRS is the required quadrilateral.)

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

** Q1 (i) ** Construct the following quadrilaterals

quadrilateral LIFT

LI = 4 cm

IF = 3 cm

TL = 2.5 cm

LF = 4.5 cm

IT = 4 cm

**Answer: **Given,

LI = 4 cm

IF = 3 cm

TL = 2.5 cm

LF = 4.5 cm (Diagonal)

IT = 4 cm (Diagonal)

Steps of construction:

Step 1. Using SSS condition ,draw

Step 2. Now, LT = TL = 2.5 cm . Using L as centre, draw an arc of radius = 2.5 cm

Step 3. Also, IT = 4 cm . Using I as centre, draw an arc of radius = 4 cm.

Step 4. Vertex T will be the point of intersection of the two drawn arcs. Join LT and TF to complete the quadrilateral.

LIFT is the required quadrilateral.

** Q1 (ii) ** Construct the following quadrilaterals

Quadrilateral GOLD

OL = 7.5 cm

GL = 6 cm

GD = 6 cm

LD = 5 cm

OD = 10 cm

**Answer: **Given,

OL = 7.5 cm

GL = 6 cm

GD = 6 cm

LD = 5 cm

OD = 10 cm

Steps of construction:

Step 1. Using SSS condition ,draw

Step 2. Now, DG = GD = 6 cm . Using D as centre, draw an arc of radius = 6 cm

Step 3. Also, LG = GL = 6 cm . Using L as centre, draw an arc of radius = 6 cm.

Step 4. Vertex G will be the point of intersection of the two drawn arcs. Join G to D and G to O to complete the quadrilateral.

GOLD is the required quadrilateral.

** Q1 (iii) ** Construct the following quadrilaterals

Rhombus BEND

BN = 5.6 cm

DE = 6.5 cm

** Answer: **Given, BEND is a rhombus.

BN = 5.6 cm (Diagonal)

DE = 6.5 cm (Diagonal)

We know that the diagonals of a rhombus bisect (cut in halves) each other at 90 degrees.

Steps of construction:

Step 1. Draw a line segment BN = 6.5 cm. With radius greater than half of BN, draw arcs on both sides of BN with B and N as the center. The line joining these two intersections is the perpendicular bisector of BN. Let it intersect BN at O (Therefore, O is the midpoint of BN. It will also be the midpoint of DE!)

Step 2. With O as the center, draw two arcs on the perpendicular bisector with radius = (Since, O is the midpoint of DE.)

Step 3. The intersecting points are vertices D and E.

Step 4. Join D to B and N. Also join E to B and N.

BEND is the required rhombus.

**NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Topic: When Two Adjacent Sides And Three Angles Are Known **

** Q1 ** Can you construct the above quadrilateral MIST if we have 100° at M instead of 75°?

** Answer: **Yes, we can draw the quadrilateral MIST if we have 100° at M instead of 75°. (It will be a different quadrilateral!)

Moreover, The vertex T will now change. And since the sum of all interior angles of a quadrilateral is 360°, hence angle T will also change.

** Answer: **Given, Two adjacent sides and three angles.

We know that sum of all the interior angles of a quadrilateral is 360°.

∠P + ∠L +∠A + ∠N= 140° + 75° + 150° + ∠N = 360°

∠N = 360° - (140° + 75° + 150°) = ** - 5° **

But this is not possible, because an angle of a quadrilateral cannot be negative.

Hence, We **cannot **construct a quadrilateral PLAN.

** Answer: **Yes, we still need at least the measure of the angle between the two adjacent sides to create a ** unique **parallelogram.

** NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise: 4.3 **

** Q1 (i) ** Construct the following quadrilaterals

Quadrilateral MORE

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

** Answer: **Given, MORE is a quadrilateral.

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

Rough:

Steps of construction:

Step 1. Draw a line segment MO = 6 cm. Construct an angle of 105° at O. As OR =4.5 cm, draw an arc with O as centre and radius = 4.5 cm. We get point R.

Step 2. Construct an angle of 105° at R.

Step 3. Construct an angle of 60° at M. This ray intersects the previous one at E.

MORE is the required quadrilateral.

** Q1 (ii) ** Construct the following quadrilaterals

Quadrilateral PLAN

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

**Answer: **Given, PLAN is a quadrilateral.

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

We know, Sum of all angles of a quadrilateral = 360°

∠P + ∠L + ∠A+ ∠N = 360° 90° + ∠L + 110° + 85° = 360°

∠L = 360° - 285° = 75°

Steps of Construction

Step 1. Draw a line segment PL = 4 cm. Construct an angle of 75° at L. As LA =6.5 cm, draw an arc with L as centre and radius = 6.5 cm. We get point A.

Step 2. Construct an angle of 110° at A.

Step 3. Construct an angle of 90° at P. This ray intersects the previous one at N.

PLAN is the required quadrilateral.

**Q1 (iii) ** Construct the following quadrilaterals

Parallelogram HEAR

HE = 5 cm

EA = 6 cm

∠R = 85°

** Answer: **Given, HEAR is a parallelogram.

HE = 5 cm

EA = 6 cm

∠R = 85°

We know, Diagonally opposite angles of a parallelogram are equal.

Therefore, ∠E = ∠R = 85°

And, Opposite sides of a parallelogram are equal and parallel to each other.

Therefore, AR = HE = 5 cm

RH = EA = 6 cm

Steps of construction:

Step 1. Draw a line segment HE = 5 cm. Construct an angle of 85° at E. As EA = 6 cm, draw an arc with O as center and radius = 6 cm. We get to point A.

Step 2. With A as centre, draw an arc of radius = AR = HE = 5 cm.

Step 3. With H as centre , draw an arc of radius = HR = EA = 6 cm. The intersection of this arc with the previous arc is R.

Step 4. Join R to H and R to A.

HEAR is the required parallelogram.

Alternatively,

Steps of construction

Step 1. Draw a line segment HE = 5 cm. Construct an angle of 85° at E. As EA = 6 cm, draw an arc with O as center and radius = 6 cm. We get to point A.

Step 2. Construct an angle of (180°-85° = 95°) at A. (Adjacent angles in a parallelogram are supplementary)

Step 3. Construct an angle of (180°-85° = 95°) at H. This ray intersects the previous one at R.

HEAR is the required parallelogram.

** Q1 (iv) ** Construct the following quadrilaterals.

Rectangle OKAY

OK = 7 cm

KA = 5 cm

** Answer: **Given, OKAY is a rectangle.

OK = 7 cm

KA = 5 cm

We know that all four angles of a rectangle are right angles ( ) and opposite sides are equal

Therefore, OK = AY = 7 cm. KA = YO = 5 cm

Steps of construction:

Step 1. Draw a line segment OK = 7 cm. Construct a right angle at K. With K a center, draw an arc of radius = 5 cm. We get to point A.

Step 2. Construct another right angle at A. With A as the center, draw an arc of radius = AY =OK = 7cm. We get the point Y.

Step 3. Join Y to O and Y to A

OKAY is the required rectangle.

** NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise: When Three Sides And Two Included Angles Are Given **

** Q1 ** In the above example, we first drew BC. Instead, what could have been be the other starting points?

** Answer: **Other than BC, we could have drawn AB or CD first.

(i) Quadrilateral ABCD with AB = 5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm and .

(ii) Quadrilateral PQRS with PQ = 4.5 cm, , ,

and .

Construct a few more examples of your own to find sufficiency/insufficiency of the

data for the construction of a quadrilateral.

** Answer: **Yes, there can be other sets of five measurements to draw a quadrilateral.

Examples:

(i) Quadrilateral ABCD with AB = 5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm and . (GIVEN)

(All 4 sides and 1 angle)

(ii) Quadrilateral PQRS having PQ = 4.5 cm, , ,

and .

(1 side, all 4 angles)

(iii) Quadrilateral ABCD with AB = 5 cm, BC = 5.5 cm, CD = 4 cm, BD = 8 cm (Included angle diagonal) and .

(3 sides, 1 included angle, and included angle diagonal)

(iv) Quadrilateral ABCD with AB = 5 cm, BC = 5.5 cm, BD = 8 cm , and

(2 sides, 2 angles (1 included), and included angle diagonal).

There can be plenty of other examples.

**NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise: 4.4 **

** Q1 (i) ** Construct the following quadrilaterals

Quadrilateral DEAR

DE = 4 cm

EA = 5 cm

AR = 4.5 cm

∠E = 60°

∠A = 90°

**Answer: **

DEAR is a quadrilateral.

DE = 4 cm

EA = 5 cm

AR = 4.5 cm

∠E = 60°

∠A = 90°

Steps of construction:

Step 1. Draw a line segment DE = 4 cm. Construct an angle of 60° at E.

Step 2. With E as centre, draw an arc of radius = EA = 5 cm. We get point A.

Step 3. Construct an angle of 90° at A. With A as centre, draw an arc of radius = AR = 4.5 cm. We get the point R.

Step 4. Join R to D.

DEAR is the required quadrilateral.

** Q1 (ii) ** Construct the following quadrilaterals

Quadrilateral TRUE

TR = 3.5 cm

RU = 3 cm

UE = 4 cm

** Answer: **TRUE is a quadrilateral.

TR = 3.5 cm

RU = 3 cm

UE = 4 cm

Steps of construction:

Step 1. Draw a line segment TR = 3.5 cm. Construct an angle of 75° at R.

Step 2. With R as a center, draw an arc of radius = OR = 3 cm. We get point U.

Step 3. Construct an angle of 120° at U. With U as a center, draw an arc of radius = UE = 4 cm. We get the point E.

Step 4. Join E to T

TRUE is the required quadrilateral.

** NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise: Some Special Cases **

** Q1 ** How will you construct a rectangle PQRS if you know only the lengths PQ and QR?

** Answer: **A rectangle is a special case of a parallelogram whose opposite sides are equal and all the angles are .

Therefore, we know all 4 sides and all 4 angles.

(Steps:

1. Draw PQ. Draw right angle at R and Q. Draw an arc of radius = QR = PS to get the points S and R.

3. Join S to R. PQRS is the required rectangle.)

** Answer:** We know, in a Kite one diagonal perpendicularly bisects the other diagonal.

Steps of construction:

Step 1. Draw a line segment AY= 8 cm. Draw the perpendicular bisector of AY.

Step 2. With Y as a center and radius = EY = 4 cm, draw an arc on one side of the perpendicular bisector. The intersection is point E.

Step 3. Again, With Y as a center and radius = SY = 6 cm, draw an arc on the other side of the perpendicular bisector. The intersection is point S.

Step 4. Join E to A and Y. And also join S to A and Y.

EASY is the required kite.

** NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise: 4.5 **

** Q1 ** The square READ with RE = 5.1 cm.

** Answer: **Given, READ is a square side RE = 5.1 cm.

We know, All the sides of a square are equal and all angles are right angles.

Therefore, RE = EA = AD = DR = 5.1 cm

Steps of construction:

Step 1. Draw a line segment RE = 5.1 cm. Construct a right angle at R and E.

Step 2. With R and E as centre, draw an arc of radius = EA = RE = 5.1 cm. We get the point D and A respectively.

Step 3. Join D to A.

READ is the required square.

** Q2 ** Draw a rhombus whose diagonals are 5.2 cm and 6.4 cm long.

** Answer: **Let ABCD be the rhombus such that:

AC = 6.4 cm (longer diagonal) and BD = 5.2 cm (shorter diagonal)

We know that the diagonals of a rhombus bisect (cut in half) each other perpendicularly, i.e at 60°

In other words, the midpoint of the diagonals coincide.

Steps of construction:

Step 1. Draw a line segment AC =6.4 cm. Now, construct the perpendicular bisector of AC. Let it intersect AC at O.

(Therefore, O is the midpoint of both the diagonals AC and BD)

Step 2. With O as center and radius half of BD = , draw two arcs on both sides of AC intersecting the perpendicular bisector at B and D.

Step 3. Join B to A and C. Also join D to A and C.

ABCD is the required rhombus.

** Q3 ** Draw a rectangle with adjacent sides of lengths 5 cm and 4 cm.

** Answer: **Let ABCD be the rectangle such that :

Where AB = 5 cm and BC = 4 cm.

We know that the opposite sides of a rectangle are equal and all the angles are 90°.

Steps of construction:

Step 1. Draw a line segment AB = 5 cm. Construct an angle of 90° at A and B.

Step 2. Construct an arc of radius =AD = BC = 4 cm with A and B as the centre . The intersection points are C and D.

Step 3. Join C to D.

ABCD is the required rectangle.

** Q4 ** Draw a parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

** Answer: **Given, OKAY is a parallelogram where OK = 5.5 cm and KA = 4.2 cm.

Steps of construction:

Step 1. Draw a line segment OK = 5.5 cm. Draw a ray KX from point K (With any suitable angle). Extend OK in the direction of KO.

Now we make a ray parallel to KX from O.

Step 2. With K as the center and a suitable radius, draw an arc cutting both OK and KX at P and Q respectively.

Step 3. With the same radius and O as the center, draw an arc cutting extended OK at P'.

Step 4. With P as the center, measure PQ using the compass. Using this as radius, cut the previous arc with P' as the center and mark it Q'. Draw a ray OZ passing through Q'.

Step 5. With radius = KA = 4.2 cm, cut two arcs on OZ and KX with O and K as centers respectively. These intersection points are Y and A respectively. Join Y to A.

OKAY is the required parallelogram. It is not unique as the angle can be varied keeping opposite sides parallel to each other.

**Practical Geometry Class 8 Maths Chapter 4-Topics**

- Constructing a Quadrilateral
- Some Special Cases

** **NCERT Solutions for Class 8 Maths: Chapter-Wise

Chapter -1 | |

Chapter -2 | |

Chapter-3 | |

Chapter-4 | Practical Geometry |

Chapter-5 | |

Chapter-6 | |

Chapter-7 | |

Chapter-8 | |

Chapter-9 | |

Chapter-10 | |

Chapter-11 | |

Chapter-12 | |

Chapter-13 | |

Chapter-14 | |

Chapter-15 | |

Chapter-16 |

### NCERT Solutions for Class 8: Subject-Wise

** How to use NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry? **

- You must have knowledge about the classification of geometric figures.
- You should go through some examples to understand the pattern of constructions.
- Once you have a clear idea, you can draw the shapes for unsolved problems given in the practice exercises.
- NCERT solutions for Class 8 Maths chapter 4 can be used to help while practicing.
*Keep working hard and happy learning!*

**Also Check NCERT Books and NCERT Syllabus here:**

## Frequently Asked Question (FAQs) - NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

**Question: **What are the important topics of chapter Practical Geometry ?

**Answer: **

Polygons, angle sum property of polygons, quadrilaterals, trapezium, parallelogram, rhombus, rectangle, and square are the important topics of this chapter.

**Question: **Which is best book for CBSE class 8 maths ?

**Answer: **

NCERT textbook is the best book for CBSE class 8 maths. You don't need to buy any supplementary book. Be though with the NCERT problems.

**Question: **Where can I find the complete solutions of NCERT for class 8 ?

**Answer: **

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

**Question: **Where can I find the complete solutions of NCERT for class 8 maths ?

**Answer: **

Here you will get the detailed NCERT solutions for class 8 maths by clicking on the link.

**Question: **Does CBSE class 8 maths is tough ?

**Answer: **

CBSE class 8 maths is damn simple and very basic math. It is a base and foundation for the upcoming classes. Most of the topics in class 8 maths are related to previous classes.

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