CBSE Class 8 Maths Practical Geometry HOTs

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