Mathematics
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
I, II and IV only
I, III and V only
I, II and V only
I, III and IV only
54. If DE = 2 cm, then BC is equal to:
4 cm
6 cm
7 cm
8 cm
55. The ratio of the perimeters of ΔADE and ΔABC is:
1 : 2
1 : 3
1 : 4
1 : 6
56. The ratio of the areas of ΔADE and trapezium DBCE is:
1 : 8
1 : 9
1 : 15
1 : 16
Related Questions
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:
ΔORC
ΔARP
ΔOBR
ΔQRP
46. ΔPQR ∼ ΔBCR by axiom:
SAS
AAA
SSS
AAS
47. If QC = 6 cm, CR = 4 cm, BR = 3 cm, then the length of RP is:
4.5 cm
5 cm
7.5 cm
8 cm
48. The ratio PQ : BC is:
2 : 3
3 : 2
2 : 5
5 : 2
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.
I and II
II and III
I and III
I, II, III and IV
50. ΔAEL is similar to:
ΔCBL
ΔCML
ΔDME
ΔBMC
51. By which axiom are the above triangles similar?
AA
SSS
SAS
ASA
52. EL : BL is equal to :
1 : 2
2 : 1
1 : 3
3 : 1
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.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
