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#### Geometry Important Questions

10th Standard EM

Reg.No. :
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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

$\cfrac { AB }{ AD } =\cfrac { AQ }{ AB }$