Practical Geometry - Worksheets

CBSE Worksheet 01
Class 08 - Mathematics (Practical Geometry)
General Instructions: All questions are compulsory. Q.1 to Q.2 carries one mark each. Q.3 to Q.7 carries two marks each. Q.8 and Q.9 carries three marks each. Q.10 to Q.12 carries four marks each.
  1. Name the special quadrilateral whose all angles and sides are equal?
  2. When does a parallelogram become a square?
  3. State True or False:
    1. The diagonals of rhombus are perpendicular and bisect each other.
    2. Opposite angles of rectangle formed at the point where diagonals meet are congruent.
    3. A rhombus can be constructed if a side and a diagonal is known.
    4. All sides of parallelogram are congruent.
  4. Fill in the blanks
    1. For any two rational numbers a and b, a × b = _________.
    2. For any three rational numbers a, b and c, a + (b + c) = _________.
    3. Reciprocal of ab where b ≠ 0 is ________.
    4. Every whole number can be written in ab where b = ________.
  5. Match the following:
    Column AColumn B
    a. Number of sides in decagoni. Rhombus
    b. Diagonals are perpendicularii. Equilateral triangle
    c. Equal sides triangleiii. Parallelogram
    d. Adjacent angles are supplementaryiv. Ten
  6. Construct a parallelogram ABCD in which AB = 4 cm, BC = 5 cm and ∠B = 60°.
  7. Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
  8. Construct a rhombus LEND where LN=5.6cm and DE=6.5cm.
  9. Construct a rectangle MIST where MI=7cm, IS=5cm.
  10. Construct a trapezium PQRS in which PQ||SR, ∠P = 105⁰, PS = 3cm, PQ = 4cm, RQ = 4.5cm and RS = 8cm.
  11. Construct Quadrilateral GOLD. OL = 7.5cm, GL = 6 cm, GD = 6 cm, LD = 5 cm, OD = 10 cm
  12. Construct a quadrilateral ABCD, with AB = 4cm, BC = 5cm, CD = 6.5cm, ∠B = 105⁰ and ∠C = ∠80⁰.

CBSE Worksheet 01
Class 08 - Mathematics (Practical Geometry)
Solution

  1. Square is the special quadrilateral whose all angles and sides are equal.
  2. When diagonals are equal and right bisectors of each other.
    1. True
    2. True
    3. False
    4. False
    1. b × a
    2. (a + b) + c OR b + (a + c)
    3. ba
    4. 1
    1. → iv
    2. → i
    3. → ii
    4. → iii
    1. Draw AB = 4 cm
    2. Draw ray BX such that ∠ABX = 60°
    3. Mark a point C such that BC = 5cm
    4. With C and A as centre, draw arcs of 4 cm & 5 cm respectively intersecting at a point D respectively
    5. ABCD is the required parallelogram.
    1. Opposite sides of a parallelogram are equal so, HO = EM = 6 cm and HE = OE = 4 cm
    2. Draw a line segment HO = 6cm.
    3. With H & O as centres draw two arcs of radii 4 cm & 3 cm respectively which meet at E.
    4. Now with, E & O as centres draw two arcs of radii 6 cm & 4 cm respectively which at M.
    5. Join HE, EM & MO. Hence HOME is the required parallelogram.
  8. Rough figure:

    Steps of construction:
    Step 1.     Draw diagonal DE = 6.5cm.
    Step 2. Draw perpendicular bisector PQ as diagonals of a rhombus are perpendicular bisectors.
    Step 3. Taking the centre point and radius as 2.8cm draw N and L on PQ.
    Step 4. Join all the points ND, DL, LE and NE.
    Hence, we get the rhombus LEND.
    Final figure:
  9. Rough figure.

    Steps of construction:
    Step 1. Draw line segment MI = 7cm.
    Step 2. With M as centre, construct an angle of 90⁰. Draw ray YM.
    Step 3. With radius as 5cm and centre as M draw an arc that lies on the above angle and mark it as T.
    Step 4. Construct 90⁰ as in step 2 and taking I as centre and radius 5cm draw an arc on the angle and name it as S.
    Step 5. Join ST.
    Hence, we get the rectangle MIST.
    Final figure:
  10. Rough figure:

    Steps of construction:
    Step 1. Draw line segment QP = 4cm.
    Step 2. With P as centre, construct an angle XPQ= 105⁰ and taking radius 3cm, draw an arc on angle and mark it as S.
    Step 3. With radius as 8cm and centre at S draw an arc
    Step 4. With Q as centre and radius 4.5cm, draw an arc intersecting the previous arc at R.
    Thus, PQRS is the required figure.
    Required Figure
  11. Steps of Construction
    1. Draw LD = 5 cm.
    2. With L as centre and radius LG = 6 cm, draw an arc.
    3. With D as centre and radius DG = 6 cm, draw another arc to intersect the arc of step 2 at G.
    4. With L as centre and radius LO = 7.5 cm, draw an arc.
    5. With D as centre and radius DO = 10 cm, draw another arc to intersect the arc of step 4 at O.
    6. Join DG, GO, OL, LG and DO.
    Then GOLD is the required quadrilateral.
  12. Rough figure:

    Steps of construction:
    Step 1. Draw line segment BC = 5cm.
    Step 2. Construct angle YBC = 105⁰ and taking B as centre and radius 4cm, draw an arc that would lie on the above angle as AB
    Step 3. On C draw angle XCB = 80⁰
    Step 4. Taking C as centre and radius 6.5cm, draw an arc that would lie on the above angle as DC.
    Step 5. Join D and A.
    Hence, we get the required quadrilateral.