Important Questions for CBSE 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 \[{\text{C,D}}\]

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 \[{\text{B}}\]

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 \[{\text{C}}\]

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 \[{\text{C}}\]

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 \[{\text{CD}}\]

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 \[{\text{CD}}\]

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\[{\text{AD}}\]

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 \[{\text{AD}}\]

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 \[{\text{BD}}\]

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 \[{\text{R,S}}\]

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.

3. 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.

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.

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