In the given figure, OD = 2 × OB, OC = 2 × OA and CD = 2 × AB then △ AOB ~ △ COD by :

1. AA

2. SS

3. SAS

4. SSS

Are the two congruent triangles always similar?

1. yes

2. no

3. none of these

If Δ ABC ∼ Δ DEF, then

1. $\dfrac{\text{AB}}{\text{EF}} = \dfrac{\text{AC}}{\text{DF}}$

2. $\dfrac{\text{AB}}{\text{DE}} = \dfrac{\text{BC}}{\text{DF}}$

3. $\dfrac{\text{AC}}{\text{DF}} = \dfrac{\text{AB}}{\text{DE}}$

4. $\dfrac{\text{BC}}{\text{EF}} = \dfrac{\text{AC}}{\text{DE}}$

Sides AB, BC and median AD of the triangle ABC are respectively proportional to sides PQ, QR and median PM of triangle PQR.

Prove that:

(i) Δ ABD ∼ Δ PQM

(ii) Δ ABC ∼ Δ PQR