#### Geometry Model Question Paper

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. In a parallelogram $\angle{A}:\angle{B}=1:2$ Then ㄥA ............

(a)

30°

(b)

60°

(c)

45°

(d)

90°

2. Which of the following is a formula to find the sum of interior angles of a quadrilateral of n-sides?

(a)

$\frac { n }{ 2 }$ $\times$ 180

(b)

$\left( \frac { n+1 }{ 2 } \right)$1800

(c)

$\left( \frac { n-1 }{ 2 } \right)$180o

(d)

(n-2)180o

3. The angle subtend by equal chords of a circle at the centre is________

(a)

Complementary

(b)

Supplementary

(c)

equal

(d)

unequal

4. The distance between the longest chord of a circle and the centre is________

(a)

1

(b)

0

(c)

2

(d)

5

5. The perpendicular line from the centre of the circle to the chord divided the chord in the ratio________

(a)

1: 1

(b)

1: 2

(c)

2: 1

(d)

1: 3

6. 5 x 2 = 10
7. In the given diagram PQRS is a parallelogram.
ㄥS = 4x - 60, ㄥQ = 30 - x. Find the angles of P and R.

8. The radius of a circle 15 cm and the length of one of its chord is 24 cm. Find the distance of the chord from the centre.

9. In a circle, AB and CD are two parallel chords with centre 0 and radius 5 em such that AB = 8 cm and CD = 6 cm determine the distance between the chords?

10. Find the value of Xo

11. Find the value of Xo

12. 5 x 3 = 15
13. In the figure find x0 and y0.

14. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

15. ABCD is a parallelogram and AP and CQ are perpendic from vertex A and C on diagonal BD. Show that
(i) ΔAPB ≅ ΔCQD
(ii) AP = CQ

16. ABCD is a rectangle and P, Q, Rand S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

17. Construct an equilateral triangle of side 6cm and locate its centroid and also its incentre. What do you observe from this?

18. 4 x 5 = 20
19. Diagonal AC of a parallelogram ABCD bisects ㄥA. Show that
(i) it bisects ㄥC also
(ii) ABCD is a rhombus.

20. Draw an equilateral triangle of side 8 cm and locate its incentre. Also draw the incircle.

21. Construct  $\triangle$ABC in which AB = BC = 8cm and $\angle$B =70o. Locate its in centre and draw the incircle

22. Draw and locate the centroid of the triangle ABC where right angle at A, AB = 8 cm and AC = 6 cm.