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#### Geometry Model Question Paper

8th Standard EM

Reg.No. :
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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.