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#### Geometry Model Question Paper

8th Standard EM

Reg.No. :
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Maths

Time : 01:30:00 Hrs
Total Marks : 50
4 x 1 = 4
1. The hypotenuse of a right angled triangle of sides 12cm and 16cm is __________.

(a)

28 cm

(b)

20 cm

(c)

24 cm

(d)

21 cm

2. The area of a rectangle of length 21 cm and diagonal 29 cm is __________cm2.

(a)

609

(b)

580

(c)

420

(d)

210

3. If the square of the hypotenuse of an isosceles right triangle is 50 cm2, the length of each
side is ____________.

(a)

25 cm

(b)

5 cm

(c)

10 cm

(d)

20 cm

4. The sides of a right angled triangle are in the ratio 5: 12: 13 and its perimeter is 120 units then, the sides are ______________.

(a)

25, 36, 59

(b)

10, 24, 26

(c)

36, 39, 45

(d)

20, 48, 52

5. 3 x 1 = 3
6. If in a Δ PQR, PR2 = PQ2 + QR2, then the right angle of Δ PQR is at the vertex ________.

()

Q

7. If 'l' and ‘m’ are the legs and 'n' is the hypotenuse of a right angled triangle then, l2 = ________.

()

n2 − m2

8. If the sides of a triangle are in the ratio 5: 12: 13 then, it is ________.

()

right angled triangle

9. 4 x 1 = 4
10. 8, 15, 17 is a Pythagorean triplet.

(a) True
(b) False
11. In a right angled triangle, the hypotenuse is the greatest side.

(a) True
(b) False
12. One of the legs of a right angled triangle PQR having ㄥR = 900 is PQ.

(a) True
(b) False
13. Pythagoras theorem is true for all types of triangles.

(a) True
(b) False
14. 7 x 2 = 14
15. Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem.
(i) 8,15,17
(ii) 12,13,15
(iii) 30, 40, 50
(iv) 9, 40, 41
(v) 24, 45, 51

16. In the figure, find PR and QR.

17. Find the distance between the helicopter and the ship.

18. From the figure,
(i) If TA = 3cm and OT = 6cm, find TG.

19. Rithika buys an LED TV which has a 25 inches screen. If its height is 7 inches, how wide is the screen? Her TV cabinet is 20 inches wide. Will the TV fit into the cabinet? Why?

20. In the figure, find MT and AH.

21. The diagonals of the rhombus is 12 cm and 16 cm. Find its perimeter.
(Hint: the diagonals of rhombus bisect each other at right angles).

22. 5 x 3 = 15
23. Can a right triangle have sides that measure 5cm, 12cm and 13cm?

24. A 20-feet ladder leans against a wall at height of 16 feet from the ground. How far is the base of the ladder from the wall?

25. Find the area of a rectangular plot of land shown in the figure.

26. Construct a parallelogram BIRD with BI = 6.5 cm, IR = 5 cm and ㄥBIR = 700. Also find its area.

27. Construct a parallelogram DUCK with DC = 8 cm, UK = 6 cm and ㄥDOU = 1100. Also find its area.

28. 2 x 5 = 10
29. Construct a trapezium BOAT in which $\overset { - }{ BO }$ is parallel to $\overset { - }{ TA }$, BO = 7 cm, OA = 6 cm, BA = 10 cm and TA = 6 cm. Also find its area.

30. Construct a trapezium DEAN in which $\overset { \_ \_ }{ DE }$ is parallel to $\overset { \_ \_ }{ NA }$, DE = 7 cm, EA = 6.5 cm ㄥEDN = 1000 and ㄥDEA = 700. Also findits area.