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Important Questions for CBSE Class 8 Maths Chapter 4 - Practical Geometry

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Last updated date: 23rd May 2024
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CBSE Class 8 Maths Important Questions for Practical Geometry - Free PDF Download

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Study Important Questions for Class 8 Maths Chapter 4 - Practical Geometry

1. Construct a Quadrilateral with four sides being 

\[{\text{AB}}\,\,{\text{ = }}\,\,{\text{4cm, BC}}\,\,{\text{ =  6cm, CD}}\,\,{\text{ = }}\,\,{\text{5}}{\text{.5cm and AD}}\,\,{\text{ = }}\,\,{\text{5cm}}\]with diagonal \[{\text{AC}}\,\,{\text{ = }}\,\,{\text{8cm}}\]

Ans: Steps for construction:

(1) Draw line \[{\text{AC}}\,{\text{ = }}\,{\text{8}}\,{\text{cm}}\]

(2) With \[{\text{A}}\]and \[{\text{C}}\]as centres draw upward arcs of  $4\;{\text{cm}}$ and $6\;{\text{cm}}$ respectively and mark 

the point they cut as \[{\text{B}}\]

(3) Join \[{\text{A}}\] and \[{\text{B}}\]

(4) Join \[{\text{C}}\]and \[{\text{B}}\]

(5) With \[{\text{A}}\]and \[{\text{C}}\]as centres draw downward arcs of  ${\text{5}}\,{\text{cm}}$ and $5.5\;{\text{cm}}$ respectively and mark the point they cut as \[{\text{D}}\]

(6) Join \[{\text{A,D}}\]and \[{\text{C,D}}\]


A quadrilateral ABCD with AB=4 cm, BC=6 cm, CD=5.5 cm, AD=5 cm


2. Construct a Quadrilateral with sides being \[{\text{AB}}\,\,{\text{ = }}\,\,{\text{4}}{\text{.0cm, BC}}\,\,{\text{ =  3}}{\text{.8cm, AD}}\,\,{\text{ = }}\,\,{\text{3}}{\text{.0cm}}\]and 

diagonal \[{\text{BD}}\,\,{\text{ = }}\,\,{\text{4}}{\text{.6cm}}\]and diagonal \[{\text{AC}}\,\,{\text{ = }}\,\,{\text{5}}{\text{.0cm}}\]

Ans: Steps for construction:

(1) Draw line \[{\text{AD}}\,{\text{ = }}\,4\,{\text{cm}}\]

(2) With \[{\text{A}}\]and \[{\text{B}}\]as centres draw arcs of  $3\;{\text{cm}}$ and $4.6\;{\text{cm}}$ respectively and mark 

the point they cut as \[{\text{D}}\]

(3) Join \[{\text{A}}\] and \[{\text{D}}\]

(4) Join \[{\text{B}}\]and \[{\text{B}}\]as dotted line

(5) With \[{\text{A}}\]and \[{\text{B}}\]as centres draw arcs of  ${\text{5}}\,{\text{cm}}$ and $3.8\;{\text{cm}}$ respectively and 

mark the point they cut as \[{\text{C}}\]

(6) Join \[{\text{A}}\]and \[{\text{C}}\]as dotted line

(7) Join \[{\text{C}}\]and \[{\text{B}}\]


A quadrilateral ABCD with AB=4 cm,BC=3.8 cm, AC=5 cm, BD=4.6 cm


3. Construct a Quadrilateral with sides being ${\text{AB}} = 3.6\;{\text{cm}},\,\,{\text{BC}} = 4\;{\text{cm}},\,\,{\text{AD}} = 5.0\;{\text{cm}}$ and 

$\angle {\text{A}} = {120^\circ }$ and $\angle {\text{B}} = {80^\circ }$.

Ans.Steps for construction:

(1) Draw the line \[{\text{AB}}\,{\text{ = }}\,{\text{3}}{\text{.6}}\,{\text{cm}}\]

(2) Make \[\angle {\text{ABX}}\,{\text{ = }}\,{\text{8}}{{\text{0}}^0}\]and make \[\angle {\text{BAY}}\,{\text{ = }}\,{\text{12}}{{\text{0}}^0}\]

(3) With \[{\text{B}}\]as centre and radius\[{\text{4}}\,{\text{cm}}\], cut off \[{\text{BC}}\,{\text{ =  4}}\,{\text{cm}}\]along \[{\text{BX}}\]

(4) With \[{\text{A}}\]as centre and radius\[{\text{5}}\,{\text{cm}}\], cut off \[{\text{AD}}\,{\text{ =  5}}\,{\text{cm}}\]along \[{\text{AY}}\]

(5) Join \[{\text{D}}\]and \[{\text{C}}\]


A quadrilateral ABCD with AB=3.6 cm, BC=4 cm, AD=5 cm


4. Construct a Quadrilateral with sides being ${\text{AB}} = 5\;{\text{cm}},\,\,{\text{BC}} = 3\;{\text{cm}},\,\,{\text{AD}} = 5.0\;{\text{cm}}$ and 

$\angle {\text{A}} = {120^\circ },\,\,\angle {\text{B}} = {80^\circ },\,\,\angle {\text{C}} = {90^\circ }$

Ans.Steps for construction:

(1) Draw the line \[{\text{AB}}\,{\text{ = }}\,5\,{\text{cm}}\]

(2) Make \[\angle {\text{ABX}}\,{\text{ = }}\,{110^0}\]and make \[\angle {\text{BAY}}\,{\text{ = }}\,{\text{12}}{{\text{0}}^0}\]

(3) With \[{\text{B}}\]as centre and radius\[3\,{\text{cm}}\], cut off \[{\text{BC}}\,{\text{ =  3}}\,{\text{cm}}\]along \[{\text{BX}}\]

(4) With \[{\text{A}}\]as centre and radius\[{\text{5}}\,{\text{cm}}\], cut off \[{\text{AD}}\,{\text{ =  5}}\,{\text{cm}}\]along \[{\text{AY}}\]

(5) Join \[{\text{D}}\]and \[{\text{C}}\]


A quadrilateral ABCD with AB=5 cm, BC=3 cm, AD=5 cm


5. Construct a Quadrilateral with sides being ${\text{AB}} = 3.8\;{\text{cm}},\,\,{\text{BC}} = 3.4\;{\text{cm}},\,\,{\text{AD}} = 5.0\;{\text{cm}}$,

${\text{CD}} = 4.5\;{\text{cm}}$ and $\angle {\text{B}} = {80^\circ }$

Ans.Steps for construction:

(1) Draw the line \[{\text{AB}}\,{\text{ = }}\,5\,{\text{cm}}\]

(2) Make \[\angle {\text{ABX}}\,{\text{ = }}\,{80^0}\] 

(3) With \[{\text{B}}\]as centre and radius\[3.4\,{\text{cm}}\], cut off \[{\text{BC}}\,{\text{ =  3}}{\text{.4}}\,{\text{cm}}\]along \[{\text{BX}}\]

(4) With \[{\text{A}}\]and \[{\text{C}}\]as centres draw arcs of  ${\text{5}}\,{\text{cm}}$ and $4.5\;{\text{cm}}$ respectively and mark the point they cut as \[{\text{D}}\]

(5) Join \[{\text{AD}}\]and \[{\text{CD}}\]


A quadrilateral ABCD with AB=3.8 cm, BC=3.4 cm, AD=5 cm


6. Construct a parallelogram with sides being $6\;{\text{cm}}$ and $4.5\;{\text{cm}}$ with one diagonal of 

length $6.8\;{\text{cm}}$

Ans.Steps for construction:

(1) Draw the line \[{\text{AB}}\,{\text{ = }}\,6\,{\text{cm}}\]

(2) With \[{\text{A}}\]and \[{\text{B}}\]as centres draw arcs of  $6.8\,{\text{cm}}$ and $4.5\;{\text{cm}}$ respectively and 

mark the point they cut as \[{\text{C}}\]

(3) Join \[{\text{AC}}\]and \[{\text{BC}}\]

(4) With \[{\text{C}}\]and \[{\text{A}}\]as centres draw arcs of  $6\,{\text{cm}}$ and $4.5\;{\text{cm}}$ respectively and mark the point they cut as \[{\text{D}}\]

(5) Join \[{\text{AD}}\]and \[{\text{CD}}\]


A parallelogram ABCD with AB=6 cm, AC=6.8 cm


7. Construct a parallelogram with one side being $5.2\;{\text{cm}}$ and two diagonals are $6\;{\text{cm}}$ 

and $6.4\;{\text{cm}}$

Ans.Steps for construction:

(1) Draw ${\text{AB}} = 5.2\;{\text{cm}}$

(2) With \[{\text{A}}\] as center and radius $3\;{\text{cm}}$, draw an arc.

(3) With ${\text{B}}$ as center and radius $3.2\;{\text{cm}}$ draw another arc, cutting the previous arc at ${\text{O}}$

(4) Join \[{\text{OA}}\]and \[{\text{OB}}\]

(5) Produce ${\text{AO}}$ to ${\text{C}}$ such that ${\text{AO}} = {\text{OC}}$ and produce ${\text{BO}}$ to ${\text{S}}$ such that ${\text{OD}} = {\text{OB}}$

(6) Join \[{\text{BC, CD}}\]and\[{\text{AD}}\]


A parallelogram ABCD with AB=5.2 cm, AC=6.4 cm, BD=6 cm


8.Construct a rectangle with its one side being $4.8\;{\text{cm}}$, and one diagonal being $6.2\;{\text{cm}}$

Ans.Steps for construction:

(1) Draw ${\text{AB}} = 4.8\;{\text{cm}}$\[{\text{BC}}\]

(2) Construct \[{90^0}\] at \[{\text{B}}\]

(3) With ${\text{B}}$ as center and radius $6.2\;{\text{cm}}$ draw an arc, cutting the perpendicular line and

mark the point as \[{\text{C}}\]

(4) Join \[{\text{BC}}\]

(5) With ${\text{C}}$as center and radius $4.8\;{\text{cm}}$draw an arc then measure and draw an arc from\[{\text{A}}\]

(6) Mark the point as \[{\text{D}}\]

(7) Join \[{\text{CD}}\] and \[{\text{AD}}\]


A rectangle ABCD with AB=4.8 cm, AC=6.2 cm


9. Construct a Rhombus two diagonals being $6.4\;{\text{cm}}$ and $10.4\;{\text{cm}}$

Ans.Steps for construction:

(1) Draw diagonal \[{\text{AC}}\]of length $10.4\;{\text{cm}}$

(2) Draw perpendicular bisector of \[{\text{AC}}\]

(3) Mark point \[{\text{O}}\]where perpendicular bisector intersects \[{\text{AC}}\]

(4) Taking $3.2\,{\text{cm}}$ as radius, and ${\text{O}}$ as center, draw an arc on top and bottom of \[{\text{AC}}\]

(5) Where arc intersects perpendicular bisector on top of \[{\text{AC}}\] is point \[{\text{D}}\]

And where it intersects perpendicular bisector on bottom of \[{\text{AC}}\] is point \[{\text{B}}\]

(6) Join \[{\text{AB,}}\,{\text{BC,}}\,{\text{CD,}}\,{\text{AD}}\]and \[{\text{BD}}\]


A rhombus ABCD with BD=6.4 cm, AC=5.2 cm


10. Construct a Rhombus with sides being $3.6\;{\text{cm}}$ and angle being ${30^\circ }$

Ans.Steps for construction:

(1) Draw line \[{\text{PS}}\,{\text{ = }}\,{\text{3}}{\text{.6 cm}}\]

(2) Construct \[{30^0}\]at \[{\text{P}}\]

(3) With \[{\text{P}}\] as centre and radius , draw an arc on ray \[{\text{P}}\]

(5) Mark the point of intersection as \[{\text{T}}\]

(6) With \[{\text{T}}\] as the centre and the same radius\[3.6{\text{ cm}}\], draw an arc

(7) With \[{\text{S}}\]as centre and same radius, draw another arc such that it intersects the previous arc at \[{\text{R}}\]

(8) Join points \[{\text{R,T}}\]and points \[{\text{R,S}}\]


A rhombus PSTR with sides 3.6 cm


Here are some of the important questions of chapter 4 - Practical Geometry. Based on these questions, try to solve these questions.


Practice Questions for Class 8 Maths Chapter 4 - Practical Geometry

  1. Construct a rectangle with one side being 8 cm, and one diagonal being 10 cm.

  2. Construct a quadrilateral whose measures are given below:

AB = 6 cm, BC = 9 cm, CD = 8.25 cm, AD = 7.5 cm.

  1. Construct a Quadrilateral with sides being AB = 6.0 cm, BC =  5.7 cm, AD = 4.5 cm and diagonal BD = 6.9 cm and diagonal AC = 7.5 cm.


To solve these questions, students must have a clear understanding of the topic discussed in the chapter. Below given is the list of topics discussed in this chapter.


Topics Included in the Class 8 Maths Chapter 4 Practical Geometry

Below-given is the list of topics discussed in Chapter 4 Practical Geometry.

 

Topic No

Topic Name

4.1

Introduction

4.2

Constructing a quadrilateral 

4.2.1

When the lengths of four sides and a diagonal are given

4.2.2

When two diagonals and three sides are given 

4.2.3

When two adjacent sides and three angles are known

4.2.4

When three sides and two included angles are given

4.3

Some special cases


Benefits of Solving the Important Questions for CBSE Class 8 Maths - Practical Geometry

Solving these important questions for CBSE Class 8 Maths Chapter 4 are very beneficial for the students. These questions are curated by the subject matter experts. Solving these questions will help students to quickly solve the NCERT textbook questions or any other reference questions and score good marks on the exam. 


Solving important questions for CBSE Class 8 Maths - Practical Geometry offers several benefits:


  • Conceptual Clarity: These questions help students understand and clarify fundamental concepts in practical geometry, ensuring a strong foundation.

  • Problem-Solving Skills: Practicing such questions enhances problem-solving skills, as students learn to apply geometric principles to real-world scenarios.

  • Exam Preparation: It prepares students for exams by familiarizing them with the types of questions that may appear in assessments.

  • Confidence Boost: Successfully solving important questions boosts students' confidence in their math abilities.

  • Retention and Application: Regular practice reinforces learning, improving long-term retention and the ability to apply geometric concepts in various situations.

  • Critical Thinking: These questions often require creative and critical thinking, fostering intellectual development.

  • Higher Scores: Mastery of important topics increases the likelihood of scoring well in exams.

  • Preparation for Advanced Topics: A strong grasp of practical geometry serves as a foundation for more advanced geometry and math topics in higher classes.


Conclusion 

Vedantu's provision of important questions for CBSE Class 8 Maths Chapter 4 - Practical Geometry is a valuable asset for students. These questions serve as a focused tool for enhancing understanding and mastering the concepts of practical geometry. Vedantu's commitment to providing these resources underscores their dedication to accessible and quality education, supporting students in their academic journey. By offering these important questions, Vedantu empowers students to not only grasp the fundamentals but also excel in their mathematical studies. They provide a targeted approach to problem-solving, ensuring comprehensive preparation for Class 8 Maths exams and laying a strong foundation for future mathematical learning.

FAQs on Important Questions for CBSE Class 8 Maths Chapter 4 - Practical Geometry

1. What is an angle?

Angle is the figure formed by joining either two rays or two line segments. Generally, it is measured in degrees. It is of two types: Positive and negative angles

2. What is quadrilateral?

A figure which has four sides and is closed in nature is called a quadrilateral. Some common quadrilaterals are square, rectangle, rhombus, and parallelogram.

3. What are "Important Questions" for CBSE Class 8 Maths Chapter 4 - Practical Geometry?

These are a set of specific questions that focus on the key concepts and topics covered in Chapter 4 of the CBSE Class 8 Maths textbook, which deals with practical geometry.

4. Why are Important Questions for CBSE Maths Chapter 4 - Practical Geometry useful for Class 8 Maths preparation?

Important questions help students prioritise their revision efforts by focusing on the most relevant topics likely to be asked in exams.

5. Are Important Questions for CBSE Class 8 Maths Chapter 4 - Practical Geometry specific to the CBSE curriculum?

Yes, these questions are designed to align with the CBSE curriculum and the content covered in the Class 8 Maths textbook.

6. Are these Important Questions for CBSE Class 8 Maths Chapter 4 - Practical Geometry available for free?

The availability of these important questions may vary. Some educational platforms offer them for free, while others may require a subscription or payment for access.

7. How can I use these Important Questions for CBSE Class 8 Maths Chapter 4 - Practical Geometry effectively for exam preparation?

These questions can be used for targeted practice and revision. Try to solve them after studying the chapter to test your understanding and reinforce your knowledge.