Q. 6

# The picture shows

AC = CE = EF = AF = 4 cm

B is midpoint of AC

AB = BC = 1/2 AC

AB = BC = 1/2 × 4 cm

AB = BC = 2 cm

Similarly,

D is midpoint of AC

CD = DE = 1/2 CE

CD = DE = 1/2 × 4 cm

CD = DE = 2 cm

AE is diagonal of ACEF,

By Pythagoras theorem,

AF2 + EF2 = AE2

42 + 42 = AE2

AE2 = 16 + 16

AE2 = 32

AE= √32

AE= 4√2 cm

J is midpoint of AE,

AJ = JE = 1/2 AE

AJ = JE = 1/2 × 4√2 cm

AJ = JE = 2√2 cm

G is midpoint of AJ,

AG = JG = 1/2 AJ

AG = JG = 1/2 × 2√2 cm

AG = JG = √2 cm

BGJH is a square

BG = JH = HB = JG = √2 cm

Also,

HD = HB = √2 cm

And,

IE = IJ = GJ =√2 cm

HD and IE are equal and parallel

HDEI is a parallelogram

HI = DE = 2 cm

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