Which of the following is correct?

1. If D is a point on side AB of ΔABC such that AD : DB = 5 : 2 and E is a point on BC such that DE ∥ AC, then ar(ΔABC) : ar(ΔDBE) = 9 : 4.

2. If the areas of two similar triangles are in the ratio 25 : 64, then their perimeters are in the ratio 5 : 8.

3.

In the adjoining figure if AB ∥ CD, then ΔAOB ∼ ΔCOD.

4.

In the adjoining figure, if D and E are the mid-points of AB and AC respectively, then ar(ΔADE) = $\dfrac{1}{2}$ × ar(ΔABC).

In the given figure, D, E and F are the mid-points of the sides BC, AC and AB respectively of ΔABC. Then which of the following does not hold true?

1. ΔAFE ∼ ΔABC

2. ΔFBD ∼ ΔABC

3. ΔEDC ∼ ΔABC

4. ΔDFE ∼ ΔABC

Directions (Q. 41 to 44): These questions are based on the following information :

In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. It is given that AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm and PQ = 2 cm.

41. The perimeter of ΔABC is:

1. 12 cm

2. 16 cm

3. 18 cm

4. 24 cm

42. The ratio of the areas of ΔAPQ and ΔABC is:

1. 1 : 3

2. 1 : 4

3. 1 : 9

4. 1 : 16

43. Which of the following holds true?

1. ΔAPQ ∼ ΔABC

2. ΔAQP ∼ ΔABC

3. ΔAPQ ∼ ΔACB

4. none of these

44. Which axiom of similarity applies in the above case?

1. AAA

2. AA

3. SSS

4. SAS

Directions (Q. 45 to 48): Using the given diagram answer the following questions.

In ΔPQR, AB ∥ QR, QP ∥ CB and AR intersects CB at O.

45. The triangle similar to ΔARQ is:

1. ΔORC

2. ΔARP

3. ΔOBR

4. ΔQRP

46. ΔPQR ∼ ΔBCR by axiom:

1. SAS

2. AAA

3. SSS

4. AAS

47. If QC = 6 cm, CR = 4 cm, BR = 3 cm, then the length of RP is:

1. 4.5 cm

2. 5 cm

3. 7.5 cm

4. 8 cm

48. The ratio PQ : BC is:

1. 2 : 3

2. 3 : 2

3. 2 : 5

4. 5 : 2