6

Q1. A parallelogram is a special kind of ………………. in which both pairs of opposite sides are parallel.

• 1) Quadrilateral
• 2) Rhombus
• 3) Square
• 4) Rectangle

Solution

A parallelogram is a special kind of quadrilateral in which both pairs of opposite sides are parallel. 

Q2. A rhombus with side 7 cm has

• 1) Each diagonal less than 14 cm
• 2) Both diagonals of the same length
• 3) Each diagonal greater than 14 cm
• 4) All angles as right angles

Solution

A rhombus with side 7 cm will have each diagonal less than 14 cm. 

Q3. If a diagonal of a quadrilateral bisects both angles, then it is a  

• 1) Rectangle
• 2) Kite
• 3) Rhombus
• 4) Parallelogram

Solution

If a diagonal of a quadrilateral bisects both angles, then it is a rhombus. 

Q4. When the opposite sides are equal and all the angles are right angles, the quadrilateral is a 

• 1) Rectangle
• 2) Trapezium
• 3) Parallelogram
• 4) Kite

Solution

When the opposite sides are equal and all the angles are right angles, the quadrilateral is a rectangle.

Q5. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ABCD taken in order is a square only if

• 1) None of these
• 2) Diagonals of ABCD are perpendicular
• 3) Diagonals of ABCD are equal
• 4) Diagonals of ABCD are equal and perpendicular

Solution

A square has equal and perpendicular diagonals.

Q6. Construct a quadrilateral ABCD where AB = 5.5 cm, CD = 2.5 cm, ∠A = 105°, ∠B = 75° and ∠C = 110°. Arrange in the proper order.  i. With A as the centre and radius 5.5cm, draw an arc to intersect AY at B.   ii. Draw ∠XAY= 105°.   iii. With B as the centre and radius 2.5cm, draw an arc to intersect BZ at C.  iv. Draw ∠ABZ = 75°. 

• 1) ii-iv-i-ii
• 2) None of the above
• 3) ii-i-iv-iii
• 4) ii-iii-i-iv

Solution

The correct order is Draw ∠XAY= 105°.  With A as the centre and radius 5.5cm, draw an arc to intersect AY at B.  Draw ∠ABZ = 75°.  With B as the centre and radius 2.5cm, draw an arc to intersect BZ at C. 

Q7. Only ____ element/s is/are enough to construct a rhombus. 

• 1) Four
• 2) Two
• 3) One
• 4) Three

Solution

Only two elements are enough to construct a rhombus.

Q8. For which of the following, both diagonals bisect each other?

• 1) Square
• 2) Kite
• 3) Quadrilateral
• 4) Trapezium

Solution

Diagonals of a square bisect each other.

Q9. A quadrilateral with 4 right angles and equal sides is called a 

• 1) Trapezium
• 2) Rectangle
• 3) Rhombus
• 4) Square

Solution

A square has equal sides and all angles are 90^o. 

Q10.

• 1) 70^o
• 2) 100^o
• 3) 80^o
• 4) 140^o

Solution

Q11. A quadrilateral whose adjacent sides are not equal is a 

• 1) Rhombus
• 2) Rectangle
• 3) Kite
• 4) Square

Solution

Adjacent sides of a rectangle are not equal.

Q12. A quadrilateral whose sides, diagonals and angles are equal is a 

• 1) Square
• 2) Rhombus
• 3) Trapezium
• 4) Rectangle

Solution

All the sides, diagonals and angles of a square are equal.

Q13. A quadrilateral with adjacent sides not equal but with angles measuring 90˚ is known as a 

• 1) Rhombus
• 2) Parallelogram
• 3) Rectangle
• 4) Square

Solution

Adjacent sides of a rectangle are not equal, but its angles measure 90˚. 

Q14. A rectangle is called an equiangular quadrilateral because

• 1) All of its angles are equal
• 2) All of its sides are equal
• 3) All of its diagonals are equal
• 4) Diagonals are equal

Solution

A rectangle is called an equiangular quadrilateral as all of its angles are equal.

Q15. A parallelogram can be constructed if

• 1) Two angles are given
• 2) Two adjacent sides and one angle are given
• 3) One side and one angle are given
• 4) One side and two angles are given

Solution

A parallelogram can be constructed if two adjacent sides and one angle are given. 

Q16. For which of the following quadrilaterals, are the diagonals equal? 

• 1) Rectangle
• 2) Kite
• 3) Rhombus
• 4) Trapezium

Solution

The diagonals of a rectangle are equal.

Q17. Construct a quadrilateral ABCD in which CA = 5.6 cm, AD = 4.5 cm, BD = 6.5 cm, CD = AD + 0.5 cm and BC = AD - 0.5 cm. Also, write the steps of construction.

Solution

Steps of Construction: (a) Draw DC = 4.5 + 0.5 = 5 cm. (b) With D as centre, draw an arc of radius 6.5 cm and with C as centre, draw an arc of radius 4 cm intersecting the previous arc at point B. Join DB and CB. (c) With D as centre and radius 4.5 cm draw an arc and with C as centre draw an arc of radius 5.6 cm intersecting the previous arc at point A. Join DA and CA. (d) Join AB. ABCD is a required quadrilateral.

Q18. Which of the following is true?

• 1) Every rectangle is a square.
• 2) None of the above.
• 3) Every rectangle is a parallelogram.
• 4) Every square is a rectangle.

Solution

Every rectangle is a square.

Q19. In a rhombus with diagonal 8 cm, each side will be ____ 4 cm.

• 1) Greater than
• 2) Smaller than
• 3) Smaller than or equal toc
• 4) Equal to

Solution

In a rhombus with diagonal 8 cm, each side will be greater than 4 cm. 

Q20. Look at the figure and write the steps which are involved in its construction.

Solution

Steps of Construction: (1) Draw PQ = 4 cm. (2) With P as centre and radius equal to 5 cm, draw an arc. (3) With Q as centre and radius equal to 3.8 cm, draw another arc, cutting the previous arc at R. (4) Join QR and PR. (5) With P as center and radius equal to 3 cm, draw an arc. (6) With Q as center and radius equal to 4.6 cm, draw another arc, cutting the previous arc at S. (7) Join PS, SQ and RS. PQRS is the required quadrilateral.

Q21. The minimum number of measurements required to construct a square is

• 1) Four
• 2) Three
• 3) Two
• 4) One

Solution

We can construct a square if the length of one of its sides or diagonals is known. 

Q22. Construct a rhombus with side 4.2 cm and one of its angles equal to 65^o.

Solution

The adjacent angle =       Steps of Construction:   i) Draw BC = 4.2 cm.   ii) Make   iii) Set off BA = 4.2 cm along BX and CD = 4.2 cm along CY   iv) Join AD   Thus, ABCD is the required rhombus.

Q23. When we make a parallelogram with adjacent sides 5 cm and a diagonal of 8 cm, we get a 

• 1) Kite
• 2) Rectangle
• 3) Square
• 4) Rhombus

Solution

When we make a parallelogram with adjacent sides 5 cm and a diagonal of 8 cm, we get a rhombus.

Q24. If EFGH is a parallelogram, then

• 1) EF is parallel to EG
• 2) EF is parallel to FG
• 3) GH is parallel to HA
• 4) EF is parallel to GH

Solution

If EFGH is a parallelogram, then EF is parallel to GH. 

Q25. Draw a parallelogram ABCD in which AB = 5 cm, AD= 4 cm, and the perpendicular distance between AB and CD is 3 cm.

Solution

  Steps of Construction:   1. Draw AB of length 5 cm   2. Make an angle of  90^o at A.   3. Cut AE = 3 cm   4. Make an angle of  90^o at E.   5. Cut AD = 4 cm to meet the ray of right angle at point D.   6. With B as center  and radius equal to 4 cm, draw an arc.   7. With D as center  and radius equal to 5 cm, draw an arc cutting the previous  arc at C.   8. Join BC and DC.   ABCD is the required parallelogram.

Q26. A quadrilateral is a rectangle if the

• 1) Opposite sides are equal in length and each angle is 90˚.
• 2) Diagonals are equal in length.
• 3) Opposite sides are equal in length.
• 4) Adjacent sides are equal in length.

Solution

A quadrilateral is a rectangle if the opposite sides are equal in length and each angle is 90˚.

Q27. In a rhombus, if the measures of one angle is 50˚, then the measure of its adjacent angle is

• 1) 130˚
• 2) 100˚
• 3) 40˚
• 4) 50˚

Solution

Adjacent angles of a rhombus are supplementary, i.e. the sum of two adjacent angles is 130˚. 

Q28. What is the maximum number of obtuse angles that a quadrilateral can have?

• 1) 3
• 2) 4
• 3) 1
• 4) 2

Solution

The maximum number of obtuse angles that a quadrilateral can have is 3

Q29. A quadrilateral is a ……………..if and only if it is both rhombus and rectangle. 

• 1) Square
• 2) Trapezium
• 3) Triangle
• 4) parallelogram

Solution

A quadrilateral is a square if and only if it is both rhombus and rectangle. 

Q30. A quadrilateral with 2 pairs of adjacent congruent sides but not all sides equal is a 

• 1) Parallelogram
• 2) Square
• 3) Trapezium
• 4) Kite

Solution

A quadrilateral with 2 pairs of adjacent congruent sidesbut not all sides equal is a kite. 

Q31. Which of the following is not the property of a parallelogram?

• 1) Rhombus
• 2) Rectangle
• 3) Trapezium
• 4) Square

Solution

A trapezium is not a parallelogram. 

Q32. If the angles of a quadrilateral are each equal to 80˚, then the fourth angle is

• 1) 140˚
• 2) 130˚
• 3) 120˚
• 4) 110˚

Solution

The sum of the angles of a quadrilateral is 360˚. 80˚ + 80˚ + 80˚ + Fourth angle = 360˚ ∴ 240˚ + Fourth angle = 360˚ ∴ Fourth angle = 360˚ - 240˚  ∴ Fourth angle = 120˚ 

Q33. Which of the following is not a quadrilateral.

• 1) Rectangle
• 2) Trapezium
• 3) Square
• 4) Triangle

Solution

A triangle has 3 sides, so it is not a quadrilateral. 

Q34. To construct a parallelogram, given the lengths of two of its diagonals, we need the measurement of at least

• 1) Three sides
• 2) Two sides
• 3) one side
• 4) Four sides

Solution

Given the length of two diagonals of a parallelogram, we need the measurement of at least one more side to construct it. 

Q35. A quadrilateral with only one pair of opposite sides parallel is called a

• 1) Rectangle
• 2) Rhombus
• 3) Trapezium
• 4) Square

Solution

A quadrilateral with only one pair of opposite sides parallel is called a trapezium.

Q36. The adjacent angles of a rhombus are ______ angles. 

• 1) supplementary
• 2) complementary
• 3) congruent
• 4) straight

Solution

The adjacent angles of a rhombus are supplementary angles. 

Q37. Construct a quadrilateral LMNO where LM = 8cm, MN = 9cm, NO=10 cm and ∠M=115° and ∠N=80°. Arrange the following in the proper order   i. Join L, M, N, O.  ii. Draw an angle of 105° at M and 80° at N.  iii. Locate L and O. iv. Draw MN.

• 1) i-ii-iv-iii
• 2) iii-ii-i-iv
• 3) iv-ii-iii-i
• 4) i-iii-iv-ii

Solution

The correct order is Draw MN. Draw an angle of 105° at M and 80° at N. Locate L and O. Join L, M, N, O. 

Q38. Construct a quadrilateral ABCD in which AB = 5.5 cm, BC = 3.5 cm,CD = 4 cm, AD = 5 cm, and ∠A = 45°.

Solution

  Steps of Construction:   1)Draw AB = 5.5 cm   2)At A, construct ∠BAK = 45°   3)Cut off AD = 5 cm from AK.   4)With B and D as centres and radii 3.5 cm and 4 cm respectively, draw two arcs cutting each other at C.   5)Join BC and DC   ABCD is the required quadrilateral.

Q39. Construct a parallelogram with 5.2cm and 4.7cm as lengths of adjacent sides and 7.6cm as the length of the diagonal connecting these given sides.  Also, write the steps of construction.

Solution

Let the required ||gm be EFGH with EF = 5.2cm and FG =4.7cm and EG = 7.6cm.     Steps of Construction: a)Draw EF = 5.2cm. b)With E is centre  and radius 7.6cm, draw an arc. c)With F as centre and radius 4.7cm, draw another arc which cuts arc of step (b) at point G. d)Join EG and FG. e)With G as centre and radius 5.2cm, draw an arc. f)With E as centre and radius 4.7cm, draw another arc which intersects the arc drawn in step (e) at H. g)Join HG and HE. EFGH is the required parallelogram.

Q40. A rectangle ABCD can be constructed if the length of

• 1) CD given
• 2) AB and DC are given
• 3) BC given
• 4) AB and AD are given

Solution

A rectangle ABCD can be constructed if the lengths of AB and AD are given. 

Q41. In a parallelogram, …………sides are congruent.

• 1) Consecutive
• 2) Opposite
• 3) Adjacent
• 4) All

Solution

In a parallelogram, opposite sides are congruent. 

Q42. For a parallelogram, which of the following statements is true? 

• 1) Diagonals are perpendicular bisectors of each other.
• 2) Diagonals are equal.
• 3) Diagonals are perpendicular.
• 4) Diagonals bisect each other.

Solution

Diagonals of a parallelogram bisect each other. 

Q43. In a square, the diagonals are

• 1) Perpendicular
• 2) All of the above
• 3) bisect each other
• 4) Congruent

Solution

In a square, the diagonals are equal and perpendicular bisectors of each other.

Q44. Construct a quadrilateral ABCD when AB = 5.2 cm, AD = 4 cm, BC = 4 cm, and

Solution

  Steps of Construction:   i) Draw AB = 5.2 cm.   ii) Make .   iii) With A as centre and radius 4 cm, draw an arc to cut AY at D.   iv) Make .   v) With B as centre and radius 4 cm, draw an arc to cut BZ at C.   vi) Join CD.   ABCD is the required quadrilateral.

Q45. What is the sum of angles of quadrilaterals?

• 1) 90°
• 2) 270°
• 3) 180°
• 4) 360°

Solution

The sum of angles of a quadrilateral is 360^o. 

Q46. A special kind of ………… is called a parallelogram. 

• 1) Polygon
• 2) Triangle
• 3) Circle
• 4) Line

Solution

A special kind of polygon is called a parallelogram. 

Q47. In a parallelogram, …………….angles are supplementary.

• 1) all
• 2) three
• 3) opposite
• 4) consecutive

Solution

In a parallelogram, consecutive angles are supplementary.

Q48. The sum of all ……………of a quadrilateral is 360˚. 

• 1) None of the above
• 2) sides
• 3) diagonals
• 4) angles

Solution

The sum of all angles of a quadrilateral is 360˚. 

Q49. A rectangle whose adjacent sides are equal is a

• 1) Rhombus
• 2) Trapezium
• 3) Kite
• 4) Square

Solution

A rectangle whose adjacent sides are equal is a square. 

Q50. Construct a rhombus ABCD, whose diagonals are of length 6 cm and 8 cm. Also, write the steps of construction.

Solution

Steps of construction: a)Draw AC = 8cm. b)Draw perpendicular bisector XY of AC meeting AC at O. c)From O cut off OD = ×6 cm = 3 cm along OX and OB = ×6 cm =3 cm along OY. d)Join AB, BC, CD, and DA. ABCD is the required rhombus.

Q51. For construction of a rhombus, we need the measures of 

• 1) One side
• 2) Two sides
• 3) One diagonal
• 4) Two diagonals

Solution

For construction of a rhombus, we need the measures of two diagonals. 

Q52. A quadrilateral whose opposite sides and all the angles are equal is a 

• 1) Trapezium
• 2) Rhombus
• 3) Rectangle
• 4) parallelogram

Solution

The opposite sides and all the angles are equal in a rectangle.

Q53. Construct a rectangle ABCD in which side BC = 5 cm and diagonal BD = 6.2 cm.

Solution

  Steps of Construction: (i) Draw BC = 5 cm.    (ii) Draw CX ⊥  BC. (iii) With B as centre and radius 6.2 cm draw an arc, cutting CX at D. (iv) Join BD. (v) With D as centre and radius 5 cm, draw an arc. (vi) With B as centre and radius equal to CD draw another arc, cutting the previous arc at A. (vii) Join AB and AD. Then, ABCD is the required rectangle.