Directions (Q. 49 to 52): Answer these questions on the basis of the following information:

Through the mid-point M of the side CD of a ∥gm ABCD, the line BM is drawn, intersecting AC on L and AD produced in E.

49. Which of the following is true for triangles BMC and EMD ?

I. They are similar to each other.

II. They are congruent to each other.

III. Their areas are equal.

IV. Their perimeters are equal.

1. I and II

2. II and III

3. I and III

4. I, II, III and IV

50. ΔAEL is similar to:

1. ΔCBL

2. ΔCML

3. ΔDME

4. ΔBMC

51. By which axiom are the above triangles similar?

1. AA

2. SSS

3. SAS

4. ASA

52. EL : BL is equal to :

1. 1 : 2

2. 2 : 1

3. 1 : 3

4. 3 : 1

Directions (Q. 53 to 56): Study the following diagram carefully and answer the given questions:

In ΔABC, D and E are points on AB and AC respectively such that AD = a, DB = 3a, AE = b and EC = 3b. DQ ∥ EA and EP ∥ DA are drawn. QP is joined.

53. ΔADE is similar to which of the following triangles?

I. ΔABC

II. ΔDAQ

III. ΔADQ

IV. ΔEPA

V. ΔEAP

1. I, II and IV only

2. I, III and V only

3. I, II and V only

4. I, III and IV only

54. If DE = 2 cm, then BC is equal to:

1. 4 cm

2. 6 cm

3. 7 cm

4. 8 cm

55. The ratio of the perimeters of ΔADE and ΔABC is:

1. 1 : 2

2. 1 : 3

3. 1 : 4

4. 1 : 6

56. The ratio of the areas of ΔADE and trapezium DBCE is:

1. 1 : 8

2. 1 : 9

3. 1 : 15

4. 1 : 16

Assertion (A): In the figure, if ∠EDB = ∠ACB, BE = 6 cm, EC = 4 cm and BD = 5 cm, then the length of AB is 12 cm.

Reason (R): If two triangles have two pairs of corresponding angles equal, then the triangles are similar.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Assertion (A): In the figure, if DE ∥ BC, then the value of x is 6 units.

Reason (R): Two similar triangles are always congruent.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.