In Fig. 6.39, ABC and AMP are two righttriangles, right angled at B and Mrespectively. Prove that:

(i) Δ ABC ~ Δ AMP

(ii)

In Fig. 6.38, altitudes AD and CE of Δ ABCintersect each other at the point P. Showthat:

(i) Δ AEP ~ Δ CDP

(ii) Δ ABD ~ Δ CBE

(iii) Δ AEP ~ Δ ADB

(iv) Δ PDC ~ Δ BEC

E is a point on the side AD produced of aparallelogram ABCD and BE intersects CD at F. Show that Δ ABE ~ Δ CFB

CD and GH are respectively the bisectorsof ∠ ACB and ∠ EGF in such a way that D and H lieon sides AB and FE of Δ ABC and Δ EFGrespectively. If Δ ABC ~ Δ FEG, show that:

(i)

(ii) Δ DCB ~ Δ HGE

(iii) Δ DCA ~ Δ HGF

In Fig. 6.40, E is a point on side CBproduced of an isosceles triangle ABCwith AB = AC. If AD ⊥ BC and EF ⊥ AC,prove that Δ ABD ~ Δ ECF