Question

正五边形ABCDE的对角线AC和BE相交于M,求证:(1)AC‖DE(2)ME=AE

Answer 1

∵正五边形,∴AB=EA,∠EAB=108°,∴∠EBA=∠BEA=36°

∵AE=BC,AB=AB,∠EAB=∠CBA,∴△EAB≌△CBA,∴∠CAB=∠EBA=36°

∴∠EMA=∠EAB=72°,ME=AD=AB