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#### Geometry Model Questions

10th Standard EM

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
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 is an isosceles triangle with $\angle$C=90o and AC = 5 cm, then AB is

(a)

2.5 cm

(b)

5 cm

(c)

10 cm

(d)

$5\sqrt { 2 }$cm

3. 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

4. A tangent is perpendicular to the radius at the

(a)

centre

(b)

point of contact

(c)

infinity

(d)

chord

5. 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°

6. 5 x 2 = 10
7. Is $\triangle$ABC~$\triangle$PQR?

8. QAand PB are perpendiculars to AB. If AO = 10 cm, BO=6 cm and PB=9 cm. Find AQ.

9. An insect 8 m away initially from the foot of a lamp post which is 6 m tall, crawls towards it moving through a distance. If its distance from the top of the lamp post is equal to the distance it has moved, how far is the insect away from the foot of the lamp post?

10. Show that  $\triangle$PST~$\triangle$PQR

11. In figure the line segment xy is parallel to side AC of $\Delta ABC$ and it divides the triangle int two parts of equal areas. Find the ratio $\cfrac { AX }{ AB }$

12. 5 x 3 = 15
13. 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

14.  DE||AC and DC||AP. Prove that $\cfrac { BE }{ CE } =\cfrac { BC }{ CP }$

15. Construct a $\triangle$PQR in which PQ=8 cm, $\angle$R=60o and the median RG from R to PQ is 5.8 cm. Find the length of the altitude from R to PQ.

16. In $AD\bot BC$ prove that AB2+CD2 = BD2+AC2

17. 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.

18. 4 x 5 = 20
19. A girl looks the reflection of the top of the lamp post on the mirror which is 66 m away from the foot of the lamppost. The girl whose height is 12.5 m is standing 2.5 m away from the mirror. Assuming the mirror is placed on the ground facing the sky and the girl, mirror and the lamppost are in a same line, find the height of the lamp post.

20. If figure OPRQ is a square and $\angle$MLN=90o. Prove that
$\triangle$LOP~$\triangle$QMO

21. A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.

22. The perpendicular from A on side BC at a $\triangle$ABC intersects BC at D such that DB = 3 CD. Prove that 2AB2 = 2AC2 + BC2.