Using midpoint to construct congruent triangles

Draw an arc with point D as the center and the length of BD as the radius, and intersect with AD at point O, so that OD=DB=CD and then connect OM and ON.

In triangle BDM and triangle ODM, because MD=MD (common side), angle BDM= angle ODM (meaning of angle bisector) and BD=OD (proof), triangle BDM congruent triangles ODM(S.A.S), BM=OM (corresponding sides in congruent triangles are equal).

In triangle CDN and triangle ODN, because ND=ND (common side), angle CDN= angle ODN (meaning of angle bisector) and CD=OD (proof), triangle CDN congruent triangles ODN(S.A.S) so CN=ON (corresponding sides of congruent triangles are equal) because OM+ON >；; MN (the sum of any two sides of a triangle is greater than the third side) is BM+CN >；; All merchant ships