In Fig. 4.103, `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 (FIGURE) ` 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

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

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 (iii) A E F ~ A D B (iv) F D C ~ B E C (FIGURE)

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 "Delta"E F G" respectively. IfDeltaA B C DeltaF E G , show that: (i) (C D)/(G H)=(A G)/(F G) (ii) DeltaD

If in two triangles A B C and D E F , (A B)/(D E)=(B C)/(F E)=(C A)/(F D) , then F D E C A B (b) F D E A B C (c) C B A F D E (d) B C A F D E

(Associativity ) Let f: A to B , g : B to C " and " h: C to . Then prove that ( h o g) o f = h o ( g o f )

In Fig. 4.128, D E F G is a square and /_B A C=90o . Prove that A G F D B G (ii) A G F E F C (FIGURE) (iii) D B G E F C (iv) D E^2=B DxxE C

E , F , G , H are respectively, the mid-points of the sides A B ,B C ,C D and D A of parallelogram A B C D . Show that the quadrilateral E F G H is a parallelogram and that its area is half the area of the parallelogram, A B C Ddot GIVEN : A quadrilateral A B C D in which L ,F ,G ,H are respectively the mid-points of the sides A B ,B C ,C D and D Adot TO PROVE : (i) Quadrilateral E F G H is a parallelogram a r(^(gm)E F G H)=1/2a r(^(gm)A B C D) CONSTRUCTION : Join A C and H F

What should come next in the following letter series ? A A B A B C A B C D A B C D E A B C D E F A B C D E F ? 1) A 2) H 3) G 4) I 5) None of these

What should come next in the following sequence ? A A B A B C A B C D A B C D E A B C D E F A B C D E F G A B C D E F G ? 1) A 2) I 3) H 4) B 5) None of these