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Geometry Important Questions

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    4 x 1 = 4
  1. If in triangles ABC and EDF,\(\cfrac { AB }{ DE } =\cfrac { BC }{ FD } \) then they will be similar, when

    (a)

    \(\angle B=\angle E\)

    (b)

    \(\angle A=\angle D\)

    (c)

    \(\angle B=\angle D\)

    (d)

    \(\angle A=\angle F\)

  2. if \(\triangle\)ABC, DE||BC, AB=3.6cm, AC=24 cm and AD=2.1 cm then the length of AE is

    (a)

    1.4 cm

    (b)

    1.8 cm

    (c)

    1.2 cm

    (d)

    1.05 cm

  3. Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

    (a)

    13 m

    (b)

    14 m

    (c)

    15 m

    (d)

    12.8 m

  4. In figure if PR is tangent to the circle at P and O is the centre of the circle, then \(\angle PQR\) is

    (a)

    120o

    (b)

    100°

    (c)

    110°

    (d)

    90°

  5. 5 x 2 = 10
  6. Is \(\triangle\)ABC~\(\triangle\)PQR?

  7. A boy of height 90cm is walking away from the base of a lamp post at a speed of 1.2m/sec. If the lamppost is 3.6m above the ground, find the length of his shadow cast after 4 seconds.

  8. An Aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after 1½ hours?

  9. Show that  \(\triangle\)PST~\(\triangle\)PQR 

  10. In figure OA· OB = OC·OD
    Show that \(\angle A=\angle C\quad and\quad \angle B=\angle D\)

  11. 4 x 5 = 20
  12. D and E are respectively the points on the sides AB and AC of a DABC such that AB=5.6 cm, AD=1.4 cm, AC=7.2 cm and AE = 1.8 cm, show that DE||BC

  13.  DE||AC and DC||AP. Prove that \(\cfrac { BE }{ CE } =\cfrac { BC }{ CP } \)

  14. In \(AD\bot BC\) prove that AB2+CD2 = BD2+AC2

  15. Prove that in a right triangle, the square of 8. the hypotenure is equal to the sum of the squares of the others two sides.

  16. 2 x 8 = 16
  17. Check whether the which triangles are similar and find the value of x.
    (i)

    (ii)

  18. In fig. if PQ||BCandPR||CD prove that

     \(\cfrac { AB }{ AD } =\cfrac { AQ }{ AB } \)

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