Question

in the adjoining figure ABCDEF is a regular hexagon prove that quadrilaterals ABDE

Answer 1

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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