Mathematics
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.
Related Questions
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
Assertion (A): In the figure, if DE ∥ BC, then the value of x is 6 units.
Reason (R): Two similar triangles are always congruent.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Assertion (A): In the figure, ∠ABC = ∠BDC = 90°.
If AD = 4 cm, BD = 6 cm, then area of ΔABC is 40 cm2.Reason (R): Areas of two similar triangles are proportional to the squares of their corresponding sides.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
