In the adjoining figure ABCDEF is a regular hexagon. Prove that quadrilateral ABDE and ACDF are parallelograms. Also prove that quadrilateral AGDH is a parallelograms
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quadrilateral ABDE , ACDF and AGDH are parallelograms if In the adjoining figure ABCDEF is a regular hexagon
Step-by-step explanation:
in Hexagon
AB = BC = CD = DE = EF = AF
∠A = ∠B = ∠C =∠D = ∠E = ∠F = 120°
ABDE
AB = DE
ΔAFE & ΔBCD
AF = BC = FE = CD
∠F = ∠C
=> ΔAFE ≅ ΔBCD
=> AE = BD
AB = DE & AE = BD
Hence Quadrilateral ABDE is a paralleogram
=> AE ║ BD => AH ║ GD
Similarly we can show ACDF is a parallelogram
AC ║ DF => AG ║ DH
AH ║ GD & AG ║ DH
=> quadrilateral AGDH is a parallelogram
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very good sir thank you fot the wonderful explanation
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