In Figure, `C D` and `G H` are respectively the medians of ` A B C` and ` E F G` . If ` A B C ~ F E G` , prove that `(i) A D C ~ F H G` `(ii) (C D)/(G H)=(A B)/(F E)` `(iii) C D B ~ G H E`

In Fig. 4.102 (i) and (ii) , if C D and G H (D\ a n d\ H lie on A B and F E ) are respectively bisectors of /_A C B and /_E G F and A B C ~ F E G , prove that (FIGURE) D C A ~ H G F (ii) (C D)/(G H)=(A C)/(F G) (iii) D C B ~ H G E

In Figure, A B=A CdotB E\ a n d\ C F are respectively the bisectors of /_B and /_C . Prove that E C B \ ~=\ F C B

In Figure, A D\ a n d\ B E are medians of A B C\ a n d\ B E||D F . Prove that C F=1/4A C .

In Figure, A D , and B E are medians of A B C and B E || D Fdot Prove that C F=1/4A Cdot

CD and GH are respectively the bisectors of /_A C B and /_E G F such that D and H lie on sides AB and FE of DeltaA B C and DeltaE F G respectively. If DeltaA B C ~DeltaF E G , show that: (i) (C D)/(G H)=(A G)/(F G) (ii) ∆ DCB ~ ∆ HGE (iii) ∆ DCA ~ ∆ HGF

If E ,F ,G and H are respectively the mid-points of the sides of a parallelogram A B C D , show that a r(E F G H)=1/2a r(A B C D)

In Fig. 4.101, A D and C E are two altitudes of A B C . Prove that A E F ~ C D F (ii) A B D ~ C B E

If E ,F ,G and H are respectively the mid-points of the sides of a parallelogram A B C D , show that a r(E F G H)=1/2a r(A B C D)dot

Identify A, B, C, D, E, F,G

In Figure, D E F G is a square and /_B A C=90 . Prove that (i) A G F ~ D B G (ii) A G F ~ E F C (iii) D B G ~ E F C (iv) D E^2=B D x E C