Geometry Book Back Questions

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
6 x 1 = 6
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. In $\angle$LMN, $\angle$L=60o,$\angle$M=50o, If $\triangle$LMN~$\triangle$PQR then the value of $\angle$R is

(a)

40o

(b)

70°

(c)

30°

(d)

110°

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. 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

5. The two tangents from an external points P to a circle with centre at O are PA and PB.If $\angle APB$=70o then the value of $\angle AOB$ is

(a)

100°

(b)

110°

(c)

120°

(d)

130°

6. 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°

7. 3 x 2 = 6
8. Is $\triangle$ABC~$\triangle$PQR?

9. If $\triangle$ABC is similar to$\triangle$DEFsuch that BC=3 cm, EF=4 cm and area of $\triangle$ABC= 54 cm2. Find the area of $\triangle$DEF.

10. Construct a triangle similar to a given triangle PQR with its sides equal to$\cfrac { 7 }{ 4 }$ of the corresponding sides of the triangle PQR (scale factor $\cfrac { 7 }{ 4 }$>1)

11. 2 x 5 = 10
12. In $\triangle$ADC=, if DE||BC, AD=x, DB=x−2, and EC=x−1 then find the lengths of the sides AB and AC.

13. 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.

14. 1 x 8 = 8
15. 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.