Geometry Model Question Paper

8th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 40
    5 x 1 = 5
  1. Two similar triangles will always have ________angles

    (a)

    acute

    (b)

    obtuse

    (c)

    right

    (d)

    matching

  2. If in triangles PQR and XYZ, \(\frac{PQ}{XY}=\frac{QR}{ZX}\) then they will be similar if

    (a)

    ∠Q=∠Y

    (b)

    ∠P=∠X

    (c)

    ∠Q=∠X

    (d)

    ∠P≡∠Z

  3. A flag pole 15 m high casts a shadow of 3 m at 10 a.m. The shadow cast by a building at the same time is 18.6 m. The height of the building is

    (a)

    90 m

    (b)

    91 m

    (c)

    92 m

    (d)

    93 m

  4. If ΔABC~ΔPQR in which ∠A = 53o and ∠Q = 77o, then R is

    (a)

    50°

    (b)

    50°

    (c)

    70°

    (d)

    80°

  5. In the figure, which of the following statements is true?

    (a)

    AB = BD

    (b)

    BD < CD

    (c)

    AC = CD

    (d)

    BC = CD

  6. 5 x 2 = 10
  7. In the given fi gure YH||TE . Prove that ΔWHY~ΔWET and also fi nd HE and TE.

  8. In the given fi gure, if ΔEAT~ΔBUN, find the measure of all angles.

  9. In the given fi gure, ∠CIP≡∠COP and ∠HIP≡∠HOP . Prove that IP ≡ OP.

  10. In the given figure if \(\frac { AO }{ OC } =\frac { BO }{ OD } =\frac { 1 }{ 2 } \) and AB=5cm. Find the value of DC.

  11. In the given figure if \(\angle \)A =\(\angle \)C then prove that \(\triangle \)AOB ~\(\triangle \)COD

  12. 5 x 3 = 15
  13. Find the unknowns in the following figures

  14. Find the unknowns in the following figures

  15. In Fig, if ΔPEN ~ ΔPAD, then find x and y.

  16. In the figure with respect to \(\triangle \)BEP and \(\triangle \)CPD prove that BP x PD = EP x PC.

  17. Two triangles BAC and BDC right angled at A and D respectively are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P. Prove that AP x PC = DP x PB.

  18. 2 x 5 = 10
  19. Construct a quadrilateral ABCD with AB=7 cm, AD=5 cm, CD = 5 cm, ∠BAC=50° and ∠ABC=60°. Also find its area.

  20. P and Q are points on sides AB and AC respectively of \(\triangle \)ABC. If AP = 3 cm PB = 6cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.

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