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ICSE Class X Math 2016 Paper

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Question : 23 of 57
Marks: +1, -0
Construct a regular hexagon of side 5 cm5\text{ cm}. Hence construct all its lines of symmetry and name them.
Solution:  
Steps of Construction :
(i) Using the given data, construct the regular hexagon ABCDEF with each side equal to 5 cm5\text{ cm}.
(ii) Draw the perpendicular bisectors of sides AB,BC,CD,DE,EFAB, BC, CD, DE, EF and FAFA which intersect ABA B at V,BCV, B C at X,CDX, C D at Y, DE at U, EF at W and FA at Z.
(iii) Join the mid points of opposite sides i.e., UV, WX and YZYZ and the diagonals passing through the centres i.e., ADAD, BEBE and CFCF.
Hence A regular hexagon has six lines of symmetry - UV, WX, YZ, AD, BE, CF.
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