CBSE 8tm maths:Construction of quadrilateral (Ch:Practical Geometry)

Point to Remember

1. .Five measurement can determine a quadrilateral uniquely.

2. A quadrilateral can be constructed uniquely if

• Its four sides and one diagonal is given.

• Its two adjacent sides and three angles are known.

• Its three sides and two included angles are given.

• Its other special properties are known (rectangle, square, rhombus, parallelogram).

• Its three sides and two diagonals given.

For more study
Construction of quadrilateral Practice Questions	(View/Read/Download)
Construction of quadrilateral  CBSE Test Paper	(View/Read/Download)
Construction of quadrilateral  CBSE Test Paper	(View/Read/Download)

1. How many measurement s can determine a quadrilateral uniquely?

Ans: 5 

2. How many measurements can determine a square? 

Ans: 1 

3. How many measurements can determine a parallelogram uniquely? 

Ans: 3 

4. How many measurement can determine a rhombus? 

Ans: 2 

5. Which property is used to construct a parallelogram. If its one side and two diagonals are given.

Ans: Diagonals are bisects to each other. 

6. What property is used to construct a rhombus. If its two diagonals are given. 

Ans: Diagonals of a rhombus bisect each other at right angle.

Practice Sample paper

Q.1. Construct a quadrilateral BDEF where DE = 4.5 cm, EF = 3.5cm, FB = 6.5cm, <F = 50 and <E = 100.

Q.2. Construct a quadrilateral ABCD give that AB = 4cm, BC = 3cm, <A = 75, <B=80  and <C=120.

Q.3. Construct a quadrilateral PQRS where PQ = 3.5 cm, QR = 6.5 cm, <P = <R = 105 and <S = 75

Q.4. Construct a quadrilateral ABCD, where BC = 5.5 cm, CD = 4.1 cm, <A = 70 ,<B = 110 and <D=85

Q.5. Construct a rhombus ABCD where AB = 6cm, <B = 75.

Q.6. Construct a rectangle WXYZ in which WX = 7cm and XY = 4cm.

Q.7. Construct a rhombus ABCD where AB = 4cm and AC = 6cm.

Q.8.Construct a square ABCD where AB = 6cm.

Q.9. Construct a parallelogram PQRS in which PQ = 4.5 cm, QR = 5.1cm and <Q=70.

Q.10. Construct a square of diagonal 6 cm long.
                                                                       OR,

Construct a parallelogram ABCD in which AC = 3.8 cm, BD = 4.6 cm and the angle between AC and BD is 60

11. Construct a parallelogram ABCD in which AB=6.5 AC=3.8 and the altitude AL from A is 2.5cm draw an altitude from C

[ Hint : Follow the given steps to construct the parallelogram ABCD.

Step 1. Draw AB = 6.5 cm.

Step 2. At A, draw AE ⊥ AB. With A as centre and radius 2.5 cm, mark an arc which intersects AE in F.

Step 3. Draw a line parallel to AB and passing through F.

Step 4. With A as centre and radius 3.4 cm, mark an arc which intersects the line parallel to AB in C.

Step 5. With C as centre and radius 6.5 cm, mark an arc which intersects the line CF in D. (Opposite sides of parallelogram are equal)

Step 6. Join BC and DA.

Thus, ABCD is the required parallelogram. 

12. Construct a quadrilateral PQRS m which PQ = 5 cm, QR = 6.5 cm, ∠P = ∠R = 100° and ∠S = 75°.

13.Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.

14. Construct a trapezium ABCD in which AB = 6 cm, BC = 4 cm, CD = 3.2 cm, ∠B = 75° and DC ∥ AB.

15. Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°.