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

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

(i) Δ ABC ~ Δ AMP

(ii)

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

Sides AB and BC and median AD of atriangle ABC are respectively proportionalto sides PQ and QR and medianPM of
Δ PQR (see Fig. 6.41). Show that
Δ ABC ~ Δ PQR.

D is a point on the side BC of a triangleABC such that ∠ ADC = ∠ BAC. Show that CA² = CB.CD