Answer:
1) By SAS theorem, ΔADE≅ΔCDF
2) By SSS theorem, ΔBDE≅ΔBDF
Step-by-step explanation:
Consider isosceles triangle ABC (see diagram).
1. In triangles ADE and CDF:
AD≅DC (since BD is median, then it divides side AC in two congruent parts);
AE≅CF (given);
∠A≅∠C (triangle ABC is isosceles, then angles adjacent to the base are congruent).
By SAS theorem, ΔADE≅ΔCDF.
2. In triangles BDE and BDF:
side BD is common;
DE≅DF (ΔADE≅ΔCDF, then congruent triangles have congruent corresponding sides);
BE≅FB (triangle ABC is isosceles, AB≅BC, AE≅CF, then BE=AB-AE, FB=BC-CF).
Be SSS theorem, ΔBDE≅ΔBDF.
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