Question

如图,△ABC中,AB=AC,∠A=120度,AB的中垂线交BC、AB于点M、N,说明MC=2BM

Answer 1

联结MA.

∵MN是AB的垂直平分线,∴MB=MA

∵AB=AC,∴∠B=∠MAB=30°,∴∠CAM=90°

又∵∠C=30°,∴在△ACM中,MC=2MA

∴MC=2MB