Refer to CBSE Class 8 Maths Practical Geometry HOTs. We have provided exhaustive High Order Thinking Skills (HOTS) questions and answers for Class 8 Mathematics Chapter 4 Practical Geometry. Designed for the 2025-26 exam session, these expert-curated analytical questions help students master important concepts and stay aligned with the latest CBSE, NCERT, and KVS curriculum.
Chapter 4 Practical Geometry Class 8 Mathematics HOTS with Solutions
Practicing Class 8 Mathematics HOTS Questions is important for scoring high in Mathematics. Use the detailed answers provided below to improve your problem-solving speed and Class 8 exam readiness.
HOTS Questions and Answers for Class 8 Mathematics Chapter 4 Practical Geometry
QUESTION BANK
1. Construct a quadrilateral ABCD such that AB = 4.5 cm, BC = 4 cm, CD= 3.9 cm, AD = 3.2cm and ∠B = 60°.
2. Construct a quadrilateral ABCD such that AB = 5 cm, BC = 4.2 cm, AD = 3.5 cm, ∠A = 90° and ∠B = 60°.
3. Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 5.6 cm, DA = 4 cm and BD = 5.4 cm.
4. Construct a quadrilateral PQRS in which PQ = 3 cm, QR = 2.5 cm, PS = 3.5 cm, PR = 4 cm and QS = 5 cm.
5. Construct a quadrilateral ABCD given that BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°.
6. Construct a parallelogram ABCD in which AB = 5.2 cm, AC = 6.5 cm and BD = 7.8 cm.
7. Construct a parallelogram ABCD in which diagonal AC = 4 cm, diagonal BD = 6 cm and angle between diagonals is 75°.
8. Construct a rectangle PQRS such that PQ = 3.5 cm and ∠RPS = 75°.
9. Construct a rectangle whose one diagonal is 6.8 cm and an angle between two diagonals is 105°.
10. Construct a rhombus BEST such that BE = 4.5 cm, ET = 6 cm.
11. Construct a rhombus whose diagonals are 7 cm and 5.3 cm.
12. Construct a square whose one diagonal is 5.8 cm.
HOTS
1. Construct a trapezium ABCD in which AB||CD and AB=9cm, CD=5cm, ∠BAD=70° and ∠DBA=50°.
2. Construct a trapezium ABCD with AB||CD where AB=6cm, CD=4cm, ∠A=70°, ∠ABD=30°.
3. Construct a trapezium ABCD in which AB||DC, AB=5cm, BC=3cm, CD=3.2cm, AD=2.8cm.
4. Construct a trapezium PQRS in which PQ || RS, PQ=8cm, QR=6cm, RS=4cm and ∠Q=60°.
5. Construct a parallelogram ABCD in which AB=6 cm, BC=4.2 cm, and the height from AB=3.5cm.
CHALLENGES
1. Construct quadrilateral according to the given measurements; the order of the letters in each case is A, B, C, D.
a. AB=4.8 cm, BC=4.4 cm, CD=7 cm, DA=3.4 cm, BD=6.2 cm.
b. AB=6.3 cm, CD=6.5 cm, BC=3.8 cm, AC=4.5 cm, AD=3.6 cm.
c. AB=CD=5.2 cm, BC=AD=3.2 cm, BD=7.2 cm.
d. AC=5.8 cm, BD=5 cm, AB=3.8 cm, BC=5.5 cm, CD=4.5 cm.
e. AC=5.8 cm, BD=5.6 cm, AB=3.5 cm, AD=4.9 cm, CD=4 cm.
f. AC=6 cm, BD=5.8 cm, AB=3.4 cm, AD=5.2 cm, BC=4.2 cm.
2. Can we construct a quadrilateral ABCD given ∠A=70°, ∠C=80°, AC=4 cm, BD=6 cm and ∠APB=110°, where P is the point of intersection of AC and BD.
3. Construct a quadrilateral ABCD with AB=2 cm, BC=3 cm, CD=4 cm and DA=5 cm and ∠B=100°, ∠C= 80°.
4. Construct parallelogram ABCD with the following measurements:
a. AD=4.2 cm, DC=5.8 cm, ∠D=43°
b. AB=4.3 cm, BC=3.2 cm, ∠C=120°
c. AD=4.2 cm, DC=5.8 cm, AC=3.4 cm
d. AD=4.3 cm, DC=5.7 cm, DB=7 cm
e. AC=6.8 cm, DB=7.6 cm, AD=6.4 cm.
5. Construct rectangles ABCD with the following data:
a. AB=4 cm, BC=6 cm
b. AB=6 cm, AC=7.2 cm
6. Construct squares ABCD:
a. which has side length 2 cm
b. which has diagonal 6 cm.
7. Construct rhombuses ABCD such that:
a. AB=3.2 cm, AC=4.8 cm
b. AB=4.4 cm, BD=5.4 cm
c. AC=7 cm, BD=4 cm
d. BD=6.8 cm, AC=5.4 cm.
8. Construct a rhombus given that the side is 5 cm long and the diagonals are in the ratio 1 : 2.
9. Is there a quadrilateral with 10 cm, 4 cm, 3 cm, 2 cm as sides. Give reason.
10. Construct a quadrilateral with sides AB=5 cm, BC=19 cm, CD=6 cm and DA=10 cm and knowing that BD also has integer length.
SUMMARY
A unique quadrilateral can be constructed only if the following five measurements are given.
1. When four sides and one diagonal are given.
2. When two diagonals and three sides are given.
3. When two adjacent sides and three angles are given.
4. When three sides and two included angles are given.
5. When four sides and one angle are given.
6. When other special properties are known.
ERROR ANALYSIS
1. Students do not draw a rough sketch. A rough sketch gives an idea of the figure to be constructed.
2. Students usually draw untidy figures.
3. Some students use pencils which are not properly sharpened and compass which is not reasonably tight. This ends up in drawing arcs of incorrect radius.
4. All the angles which are multiples of 15° must be drawn using only compass but the students draw the angles with the help of a protractor.
5. The figures should be labelled properly with the lengths of sides and angles marked. At times the students just draw the figure which is not labelled.
6. Steps of construction should be written only if asked.
ACTIVITY
Solve the following crossword puzzle, hints are given below: 
Across
1. A plane figure bound by four straight lines.
Answer: Quadrilateral
3. Drawing a geometrical figure by using a ruler and compass as geometrical instruments.
Answer: Construction
8. Line segment which can be extended in both the directions.
Answer: Line
Down
2. In a rectangle, all ________________ are equal.
Answer: Angles
4. A plane figure bound by three straight lines.
Answer: Triangle
5. Two lines that are always at the same distance.
Answer: Parallel
6. Part of a circle between any two points on it.
Answer: Arc
7. Construction of parallelogram ABCD is possible when the measure of the consecutive sides and one _____________ is given.
Answer: Diagonal
Important Practice Resources for Class 8 Mathematics
HOTS for Chapter 4 Practical Geometry Mathematics Class 8
Students can now practice Higher Order Thinking Skills (HOTS) questions for Chapter 4 Practical Geometry to prepare for their upcoming school exams. This study material follows the latest syllabus for Class 8 Mathematics released by CBSE. These solved questions will help you to understand about each topic and also answer difficult questions in your Mathematics test.
NCERT Based Analytical Questions for Chapter 4 Practical Geometry
Our expert teachers have created these Mathematics HOTS by referring to the official NCERT book for Class 8. These solved exercises are great for students who want to become experts in all important topics of the chapter. After attempting these challenging questions should also check their work with our teacher prepared solutions. For a complete understanding, you can also refer to our NCERT solutions for Class 8 Mathematics available on our website.
Master Mathematics for Better Marks
Regular practice of Class 8 HOTS will give you a stronger understanding of all concepts and also help you get more marks in your exams. We have also provided a variety of MCQ questions within these sets to help you easily cover all parts of the chapter. After solving these you should try our online Mathematics MCQ Test to check your speed. All the study resources on studiestoday.com are free and updated for the current academic year.
You can download the teacher-verified PDF for CBSE Class 8 Maths Practical Geometry HOTs from StudiesToday.com. These questions have been prepared for Class 8 Mathematics to help students learn high-level application and analytical skills required for the 2025-26 exams.
In the 2026 pattern, 50% of the marks are for competency-based questions. Our CBSE Class 8 Maths Practical Geometry HOTs are to apply basic theory to real-world to help Class 8 students to solve case studies and assertion-reasoning questions in Mathematics.
Unlike direct questions that test memory, CBSE Class 8 Maths Practical Geometry HOTs require out-of-the-box thinking as Class 8 Mathematics HOTS questions focus on understanding data and identifying logical errors.
After reading all conceots in Mathematics, practice CBSE Class 8 Maths Practical Geometry HOTs by breaking down the problem into smaller logical steps.
Yes, we provide detailed, step-by-step solutions for CBSE Class 8 Maths Practical Geometry HOTs. These solutions highlight the analytical reasoning and logical steps to help students prepare as per CBSE marking scheme.