In the given Fig.  and ∠1 = ∠2, show that ∆PQS ~ ∆TQR.

193. S and T are points on sides PR and QR of ∆PQR such that ∠P = ∠RTS. Show that ∆RPQ ~ ∆RTS.

In the given fig, if  show that .

In the given Fig, altitudes AD and CE of  intersects each other at the point P. Show that:
(i) ∆AEP ~ ∆CDP
(ii) ∆ABD ~ ∆CBE
(iii) ∆AEP ~ ∆ADB
(iv) ∆PDC ~ ∆BEC.

In the given fig, ABC and AMP are two right triangles, right angled at B and M respectively.
Prove that:
(i)   
(ii) 

CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ~ ΔFEG, show that:
(i)     
(ii)    
(iii) 
             

In the given fig, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC. Prove that ∆ABD ~ ∆ECF.