Q29 of 77 Page 15

In Fig. 15.90, D and E are two points on BC such that BD=DE=EC. Show that ar(Δ ABD) = ar(Δ ADE) =ar(Δ AEC)

Draw a line through A parallel to BC

Given that,


BD = BE = EC


We observed that the triangles ABD and AEC are on the same base and between the same parallels l and BC


Therefore, their areas are equal


Hence,


Area () = Area () = Area ()


More from this chapter

All 77 →
27

In Fig. 15.89, ABCD is a ||gm. O is any point on AC. PQ||AB and LM||AD. Prove that:


ar(||gm DLOP) = ar(||gm BMOQ)

 28

In a Δ ABC, if L and M are points on AB and AC respectively such that LM||BC. Prove that:

(i) ar(Δ LCM) = ar(Δ LBM)


(ii) ar(Δ LBC) = ar(Δ MBC)


(iii) ar(Δ ABM) = ar(Δ ACL)


(iv) ar(Δ LOB) = ar(Δ MOC)

 30

In Fig. 15.91, ABC is a right triangle right angled at A, BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX⊥ DE meets BC at Y. Show that:


(i) Δ MBC ≅ ABD (ii) ar(BYXD) =2ar(Δ MBC)


(iii) ar(BYXD) = ar(ABMN)


(iv) Δ FCB ≅ Δ ACE


(v) ar(CYXE) = 2ar(Δ FCB)


(vi) ar(CYXE) = ar(ACFG)


(vii) ar(BCED) = ar(ABMN)+ ar(ACFG)

 1

If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find